Showing 1–50 of 97 results for author: Nasu, J

Chiral bosonic mean-field Ansatz and spin dynamics in spin-1 Kitaev magnets

Authors: Daiki Sasamoto, Arnaud Ralko, Jaime Merino, Joji Nasu

Abstract: The Kitaev model is a paradigmatic system for realizing quantum spin liquids, but its higher-spin extensions are not exactly solvable, and their spin dynamics is less well understood than in the spin-1/2 case. In this work, we reexamine a previously introduced triplet-pairing $φ_t = π/2$ phase pattern for the antiferromagnetic $S = 1$ Kitaev model and extend the analysis to weak symmetric off-diag… ▽ More The Kitaev model is a paradigmatic system for realizing quantum spin liquids, but its higher-spin extensions are not exactly solvable, and their spin dynamics is less well understood than in the spin-1/2 case. In this work, we reexamine a previously introduced triplet-pairing $φ_t = π/2$ phase pattern for the antiferromagnetic $S = 1$ Kitaev model and extend the analysis to weak symmetric off-diagonal exchanges $Γ$ and $Γ'$. Using a bond-operator formulation of Schwinger-boson mean-field theory, we calculate the dynamical spin structure factor for the triplet 0-flux and triplet $π/2$-flux Ansätze with a spin-correlation scheme appropriate for Kitaev interactions. In the pure Kitaev limit, the $π/2$-flux Ansatz yields a flatter spectrum than the 0-flux Ansatz. The real-space spin correlations show that the $π/2$-flux Ansatz suppresses longer-distance correlations more strongly than the 0-flux Ansatz, yielding a correlation pattern closer to the short-ranged form expected in the Kitaev limit. This comparison shows that the flatness of $S(\boldsymbol{q}, ω)$ is tied to short-ranged spin correlations and is therefore an important consistency check, although it is not, by itself, a diagnostic of time-reversal-symmetry breaking. We then study weak off-diagonal exchanges along $Γ' = Γ$ near the pure Kitaev limit, taking the same-sign relation from analyses of candidate spin-1 Kitaev materials. Gapped solutions are obtained within the constrained $π/2$-flux manifold, and the spectra share the qualitative energy- and momentum-space features found by finite-size exact diagonalization. Taken together, these results support the triplet $π/2$-flux chiral bosonic Ansatz as a useful mean-field description of spin dynamics near the antiferromagnetic $S = 1$ Kitaev limit with weak off-diagonal exchanges. △ Less

Submitted 19 August, 2026; originally announced August 2026.

Comments: 21 pages, 11 figures

Halogen control of magnetic competition in Kitaev candidate Ru$X_3$ ($X =$ Cl, Br)

Authors: Ryuta Iwazaki, Shinnosuke Koyama, Takashi Koretsune, Shintaro Hoshino, Joji Nasu

Abstract: The spin-orbital Mott insulators Ru$X_3$ ($X =$ Cl, Br) have attracted considerable attention as promising candidate materials for realizing a Kitaev spin liquid. In this study, we construct effective pseudospin models from multiorbital Hubbard models derived from first-principles calculations and investigate the magnetic states of RuCl$_3$ and RuBr$_3$. From the constructed effective models, we f… ▽ More The spin-orbital Mott insulators Ru$X_3$ ($X =$ Cl, Br) have attracted considerable attention as promising candidate materials for realizing a Kitaev spin liquid. In this study, we construct effective pseudospin models from multiorbital Hubbard models derived from first-principles calculations and investigate the magnetic states of RuCl$_3$ and RuBr$_3$. From the constructed effective models, we find that RuBr$_3$ has more extended Wannier orbitals and stronger interlayer exchange interactions than RuCl$_3$. These interactions enhance three-dimensional correlations, consistent with the stronger antiferromagnetic tendency experimentally inferred for RuBr$_3$. Orbital-dependent Coulomb anisotropy further reduces the energy difference between ferromagnetic and zigzag states. Our results clarify how halogen substitution controls magnetic competition in Ru$X_3$ through interlayer exchange interactions and effects of orbital-dependent Coulomb interactions. △ Less

Submitted 14 July, 2026; originally announced July 2026.

Comments: 17 pages, 11 figures

Three-dimensional zigzag correlations in the van der Waals Kitaev magnet RuBr$_3$

Authors: H. Gretarsson, R. Iwazaki, F. Sato, H. Gotou, S. Francoual, J. Nasu, Y. Imai, K. Ohgushi, J. Chaloupka, B. Keimer, H. Suzuki

Abstract: Ruthenium trihalides Ru$X_3$ ($X$ = Cl, Br, I) provide a tunable platform for Kitaev magnetism in two-dimensional van der Waals materials. Despite their similar crystal structures and zigzag antiferromagnetic order, RuBr$_3$ exhibits a higher Néel temperature ($T_N$) than RuCl$_3$, suggesting their distinct proximity to the Kitaev quantum spin liquid phase. Using Ru $L_3$-edge resonant x-ray scatt… ▽ More Ruthenium trihalides Ru$X_3$ ($X$ = Cl, Br, I) provide a tunable platform for Kitaev magnetism in two-dimensional van der Waals materials. Despite their similar crystal structures and zigzag antiferromagnetic order, RuBr$_3$ exhibits a higher Néel temperature ($T_N$) than RuCl$_3$, suggesting their distinct proximity to the Kitaev quantum spin liquid phase. Using Ru $L_3$-edge resonant x-ray scattering, we show that, while the long-range zigzag order in RuBr$_3$ disappears at $T_N$, the zigzag correlations that persist well above $T_N$ show a pronounced spectral weight redistribution along the interlayer direction. These results suggest that the enhanced interlayer magnetic interactions driven by the extended Br 4$p$ orbitals stabilize three-dimensional zigzag correlations in RuBr$_3$. △ Less

Submitted 6 April, 2026; originally announced April 2026.

Dynamical spin correlations in kagome antiferromagnets: comparison of Abrikosov fermion and Schwinger boson approaches beyond mean field

Authors: Daiki Sasamoto, Joji Nasu

Abstract: Quantum spin liquids exhibit fractionalized spin excitations as a consequence of strong quantum many-body effects. The kagome antiferromagnetic Heisenberg model is a promising candidate for a quantum spin-liquid ground state; however, the nature of its excitation spectrum remains controversial, particularly regarding the presence of a spin gap and the gauge structure coupled to fractional quasipar… ▽ More Quantum spin liquids exhibit fractionalized spin excitations as a consequence of strong quantum many-body effects. The kagome antiferromagnetic Heisenberg model is a promising candidate for a quantum spin-liquid ground state; however, the nature of its excitation spectrum remains controversial, particularly regarding the presence of a spin gap and the gauge structure coupled to fractional quasiparticles. To address these issues, parton approaches have been extensively employed, where spin operators are represented in terms of fermionic or bosonic quasiparticles within the Abrikosov fermion and Schwinger boson frameworks. Thus far, these approaches have been pursued independently, and it has remained unclear how the results obtained from these frameworks compare, particularly with respect to the spin dynamics and gauge structure of the kagome antiferromagnet. Here, we investigate the dynamical spin structure factor of the antiferromagnetic Heisenberg model with a Dzyaloshinskii-Moriya interaction on the kagome lattice, relevant to herbertsmithite, by employing both approaches. We find that the dynamical spin structure factor obtained from the Abrikosov fermion mean-field theory exhibits dome-shaped features, and that its continuum structure significantly depends on the gauge structure of the spin-liquid ansatz. On the other hand, the Schwinger boson mean-field theory yields a concave-down structure in the low-energy region, distinct from that obtained using the Abrikosov fermion approach. Moreover, incorporating many-body effects beyond the mean-field approximation substantially reduces the low-energy gap and enhances the low-energy spectral weight, consistent with experimental observations. Our results suggest the importance of many-body effects in the Schwinger boson theory for capturing the low-energy spin dynamics of kagome antiferromagnets. △ Less

Submitted 2 July, 2026; v1 submitted 22 March, 2026; originally announced March 2026.

Comments: 32 pages, 16 figures

Journal ref: Phys. Rev. B 114, 074405 (2026)

Quantum signal processing in Hilbert space fragmented systems

Authors: Naoya Egawa, Kaoru Mizuta, Joji Nasu

Abstract: Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to nonequilibrium control in integrable many-body systems, enabling the realization of nonequilibrium dynamics with greater flexibility than Floquet engineering. Howe… ▽ More Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to nonequilibrium control in integrable many-body systems, enabling the realization of nonequilibrium dynamics with greater flexibility than Floquet engineering. However, extending QSP to nonintegrable systems faces fundamental obstacles arising from the limited number of conserved quantities and thermalization. In this work, we propose a protocol that leverages QSP in systems exhibiting Hilbert space fragmentation (HSF). Specifically, we consider a pair-hopping model with four-fold periodic potentials that exhibits an HSF structure, thereby providing integrable and nonintegrable sectors within a single system. We analytically show that nonequilibrium dynamics can be flexibly designed through QSP engineered by these potentials in the integrable sectors. In contrast, we numerically identify signatures of thermalization in the nonintegrable sectors. Remarkably, by inserting domain walls, we achieve parallel control of multiple quantum dynamics within a single system. This approach sheds light on the control of nonequilibrium dynamics from the perspective of quantum computation by extending the scope of QSP to nonintegrable systems. △ Less

Submitted 17 March, 2026; originally announced March 2026.

Comments: 10 pages, 5 figures

Formulation of intrinsic nonlinear thermal conductivity for bosonic systems using quantum kinetic equation

Authors: Aoi Kuwabara, Joji Nasu

Abstract: Nonlinear responses in transport phenomena have attracted significant attention because they can arise even when linear responses are forbidden by symmetry, with the quantum geometry of Bloch wave functions playing an essential role. While such effects have been extensively studied in electric transport, similar quantum-geometric mechanisms are also expected to govern nonlinear thermal transport.… ▽ More Nonlinear responses in transport phenomena have attracted significant attention because they can arise even when linear responses are forbidden by symmetry, with the quantum geometry of Bloch wave functions playing an essential role. While such effects have been extensively studied in electric transport, similar quantum-geometric mechanisms are also expected to govern nonlinear thermal transport. In particular, thermal responses are crucial in bosonic systems such as magnons and phonons, which are charge-neutral quasiparticles. However, a consistent theoretical description of nonlinear thermal transport remains challenging because of the difficulty in the treatment of energy magnetization in higher-order responses with Luttinger's gravitational potential method. Here, we formulate the intrinsic nonlinear thermal conductivity of bosonic systems using a quantum kinetic equation approach that avoids Luttinger's method and naturally incorporates contributions from energy magnetization. We identify three distinct contributions to the nonlinear thermal conductivity: two expressed in terms of quantum-geometric quantities, namely the quantum metric and the thermal Berry-connection polarizability (TBCP), and a third determined solely by the band dispersions. Applying our formalism to a specific quantum spin model within linear spin-wave theory, we show that the TBCP term dominates the nonlinear thermal Hall effect in the absence of threefold symmetry. Our results differ quantitatively from those obtained using semiclassical theory, thereby highlighting the importance of quantum corrections beyond the semiclassical picture. These findings establish a general framework for intrinsic nonlinear thermal responses in bosonic systems and reveal quantum-geometric mechanisms underlying thermal transport beyond linear response theory. △ Less

Submitted 8 August, 2026; v1 submitted 11 March, 2026; originally announced March 2026.

Comments: 33 pages, 8 figures

Journal ref: Phys. Rev. B 114, 105107 (2026)

Schwinger boson theory for $S=1$ Kitaev quantum spin liquids

Authors: Daiki Sasamoto, Joji Nasu

Abstract: The Kitaev model is an exactly solvable model with a quantum spin liquid ground state. While this model was originally proposed as an $S=1/2$ spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the $S=1/2$ case, such higher-$S$ models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite… ▽ More The Kitaev model is an exactly solvable model with a quantum spin liquid ground state. While this model was originally proposed as an $S=1/2$ spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the $S=1/2$ case, such higher-$S$ models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite temperatures. Here, we focus on the $S=1$ Kitaev model, which is proposed to host bosonic quasiparticles. We investigate this model using Schwinger boson mean-field theory, introducing bosonic spinons as fractional quasiparticles by extending bond operators to address anisotropic spin interactions. We determine the mean-field parameters that realize a quantum spin liquid in both ferromagnetic and antiferromagnetic Kitaev models. Based on this ansatz, we calculate dynamical and equal-time spin structure factors. We find that the conventional scheme based on Wick decoupling with respect to spinons to calculate spin correlations, the resultant spin structure factors exhibit a momentum dependence that is not consistent with the sign structure expected from the exchange interaction. To resolve this issue, we propose an alternative evaluation based on decoupling with respect to bond operators. We demonstrate that, in our scheme, this discrepancy is removed, and the momentum dependence of the spin structure factors is consistent with the sign of the exchange constant. We also compute the temperature evolution of the dynamical spin structure factor and find that the zero-temperature continuum splits into two distinct structures as temperature increases, which can be understood in terms of the bandwidth narrowing of spinons. Finally, we clarify why the two decoupling schemes result in different momentum dependences and discuss their relationship to previous studies. △ Less

Submitted 24 June, 2026; v1 submitted 30 September, 2025; originally announced September 2025.

Comments: 22 pages, 12 figures

Journal ref: Phys. Rev. Research 8, 033138 (2026)

Thermal Hall transport in Kitaev spin liquids

Authors: Tsuyoshi Okubo, Joji Nasu, Takahiro Misawa, Yukitoshi Motome

Abstract: We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature, $κ_{xy}/T$, significantly overshoots the value of the half-integer quantization and exhibits a pronounced h… ▽ More We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature, $κ_{xy}/T$, significantly overshoots the value of the half-integer quantization and exhibits a pronounced hump while decreasing temperature. Moreover, we show that the field-direction dependence of $κ_{xy}/T$ is consistent with the sign of the Chern number associated with the Majorana fermions across a wide range of magnetic fields. We also demonstrate that the additional off-diagonal interactions, known as the $Γ$ and $Γ^{\prime}$ terms, considerably affect $κ_{xy}/T$. In particular, we show that positive $Γ$ and negative $Γ^{\prime}$ lead to a remarkable enhancement in the intermediate temperature region. From the comparison with the classical counterpart, we reveal that the effects of the $Γ$ term go beyond the classical picture, indicating significant quantum fluctuation effects, while those of the $Γ^\prime$ term are well captured at the classical level. These comprehensive analyses indicate that the enhanced thermal Hall response is consistently explained by dominant contributions from topological Majorana fermions, even within the polarized regime beyond the critical field. Our approach not only establishes a robust theoretical framework for understanding the thermal Hall transport in Kitaev materials such as $α$-RuCl$_{3}$, but also offers a promising pathway to bridge the gap between theories and experiments across a wide range of strongly correlated materials. △ Less

Submitted 2 September, 2025; v1 submitted 22 July, 2025; originally announced July 2025.

Comments: 26 pages, 26 figures

Formulation of spin Nernst effect for spin-nonconserving insulating magnets

Authors: Shinnosuke Koyama, Joji Nasu

Abstract: The spin Nernst effect, an antisymmetric response of a spin current to a temperature gradient, has attracted attention as spin transport phenomenon arising from the topologically nontrivial band structure of carriers. This effect can occur not only in itinerant electron systems but also in localized electron systems that emerge due to electronic correlations. In such systems, elementary excitation… ▽ More The spin Nernst effect, an antisymmetric response of a spin current to a temperature gradient, has attracted attention as spin transport phenomenon arising from the topologically nontrivial band structure of carriers. This effect can occur not only in itinerant electron systems but also in localized electron systems that emerge due to electronic correlations. In such systems, elementary excitations behaving as bosons govern spin transport, and magnetic interactions originating from spin-orbit coupling can induce a topologically nontrivial band structure. However, such magnetic interactions can potentially break spin conservation, thereby preventing conventional spin currents from being conserved. In this study, starting from a general localized electron model, we formulate the spin Nernst effect in terms of a conserved spin current that remains applicable even in spin-nonconserving systems. To address the torque term appearing in the conserved spin current, we adopt semiclassical theory and derive an expression for the spin Nernst coefficient for bosonic systems. This coefficient consists of two terms originating from the Berry curvature and the quantum metric, which are distinctly different from the spin Berry curvature obtained in an approach that neglects the torque term. We apply our framework to two specific quantum spin models, the Kitaev-Heisenberg and Shastry-Sutherland models, and calculate the temperature dependence of the spin Nernst coefficient. We find that this quantity significantly differs from that obtained by neglecting the torque term in both models. Furthermore, we clarify that the impact of the torque term on the spin Nernst effect strongly depends on the model parameters, suggesting that our formulation based on the conserved spin current is essential for understanding this effect in insulating magnets. △ Less

Submitted 8 August, 2025; v1 submitted 13 March, 2025; originally announced March 2025.

Comments: 28 pages, 9 figures

Journal ref: Phys. Rev. B 112, 014447 (2025)

Magnetic-field effect on excitonic condensation emergent in extended Falicov-Kimball model

Authors: Naoya Ohta, Joji Nasu

Abstract: We investigate the effects of magnetic fields on excitonic condensation in the extended Falicov-Kimball model, which is a spinless two-orbital Hubbard model with orbital splitting. In lattice systems under magnetic fields up to several tens of teslas, Zeeman effects on electron spins have been extensively studied, while the impact on orbital motion has often been considered negligible. However, th… ▽ More We investigate the effects of magnetic fields on excitonic condensation in the extended Falicov-Kimball model, which is a spinless two-orbital Hubbard model with orbital splitting. In lattice systems under magnetic fields up to several tens of teslas, Zeeman effects on electron spins have been extensively studied, while the impact on orbital motion has often been considered negligible. However, the recent capability to generate ultra-high magnetic fields exceeding 1000 T has renewed interest in understanding their influence on ordered phases in correlated electron systems, beyond spin-related phenomena. To examine these effects, we incorporate a magnetic field into the extended Falicov-Kimball model by introducing the Peierls phase into the transfer integrals, enabling the study of orbital motion. Using the Hartree-Fock approximation, we reveal a nonmonotonic response of the excitonic order parameter to increasing magnetic fields. At sufficiently high fields, the excitonic order is suppressed, resulting in a disordered insulating state characterized by partial occupation of the two orbitals with nonzero Chern numbers. This state is distinct from a fully orbital-polarized configuration. Furthermore, our analysis of an excitonic supersolid phase, in which excitonic and orbital orders coexist, demonstrates that orbital order remains robust under magnetic fields, while excitonic condensation is suppressed. These findings provide insights into the interplay between orbital motion and magnetic fields in multi-orbital correlated electron systems. △ Less

Submitted 15 April, 2025; v1 submitted 16 January, 2025; originally announced January 2025.

Comments: 12 pages, 8 figures

Journal ref: J. Phys. Soc. Jpn. 94, 054702 (2025)

Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators

Authors: Naoya Egawa, Kaoru Mizuta, Joji Nasu

Abstract: Discrete time crystals (DTCs) have emerged as novel nonequilibrium phases of matter that spontaneously break discrete time-translation symmetry in periodically driven systems. Rigorous experimental validation of DTCs, which requires highly controllable quantum simulators, has stimulated extensive research across diverse fields in condensed matter physics and quantum information technologies. Among… ▽ More Discrete time crystals (DTCs) have emerged as novel nonequilibrium phases of matter that spontaneously break discrete time-translation symmetry in periodically driven systems. Rigorous experimental validation of DTCs, which requires highly controllable quantum simulators, has stimulated extensive research across diverse fields in condensed matter physics and quantum information technologies. Among these advances, DTCs were demonstrated in a hybrid spin register within diamond, comprising a processor spin and surrounding memory spins. However, in conventional strategies involving a bias magnetic field, the field application effectively restricts the controllability of the processor spin. This limitation can be a significant barrier to the next goal of DTCs: achieving multifunctionality through enhanced local controllability. In this study, we theoretically propose multiple DTC protocols through the design of specific single-site control within the entire system. To this end, we consider a concrete model of a diamond-based quantum simulator operating without a bias magnetic field, thereby eliminating the restrictions on the processor spin. Our findings demonstrate that single-site operations enable access to DTCs with multiple distinct features in terms of periodicity and lifetime. Therefore, this approach provides a promising platform for creating diverse DTCs induced by single-site operations. △ Less

Submitted 10 December, 2024; originally announced December 2024.

Comments: 16 pages, 3 figures

Journal ref: Phys. Rev. B 111, 144311 (2025)

Impact of triplon damping on thermal Hall conductivity in Shastry-Sutherland model

Authors: Shinnosuke Koyama, Joji Nasu

Abstract: We investigate the thermal Hall effect in the Shastry-Sutherland model, incorporating interactions between quasiparticle excitations. In this model, with strong nearest-neighbor interactions, the ground state is well described by the direct product of spin-singlet states, and the elementary excitations to spin-triplet states are known as triplons. In candidate materials for this model, Dzyaloshins… ▽ More We investigate the thermal Hall effect in the Shastry-Sutherland model, incorporating interactions between quasiparticle excitations. In this model, with strong nearest-neighbor interactions, the ground state is well described by the direct product of spin-singlet states, and the elementary excitations to spin-triplet states are known as triplons. In candidate materials for this model, Dzyaloshinskii-Moriya interactions are inevitably present, resulting in topologically non-trivial band structures for triplon excitations. In this study, we examine quasiparticle damping due to triplon-triplon interactions as a potential factor contributing to the suppression of the thermal Hall effect. We apply nonlinear flavor-wave theory to the Shastry-Sutherland model and treat triplons as bosonic excitations. We calculate the triplon damping rate using the imaginary Dyson equation approach and evaluate the thermal Hall conductivity. Our findings demonstrate that triplons with nonzero Berry curvature are scattered by thermally excited triplons. This scattering effect suppresses the thermal Hall conductivity, particularly at finite temperatures, highlighting the significant role of triplon damping in the thermal Hall effect. △ Less

Submitted 15 November, 2024; originally announced November 2024.

Comments: 11 pages, 6 figures

Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation

Authors: Chihiro Harada, Atsushi Ono, Joji Nasu

Abstract: Quantum spin liquids realized in the Kitaev model offer a platform for fractionalization of spin into two quasiparticles: itinerant Majoranas and localized visons. Introducing a uniform weak magnetic field associates a Majorana zero mode with each vison excitation. The vison accompanied by a Majorana zero mode is known to behave as a non-Abelian anyon, which has garnered significant attention for… ▽ More Quantum spin liquids realized in the Kitaev model offer a platform for fractionalization of spin into two quasiparticles: itinerant Majoranas and localized visons. Introducing a uniform weak magnetic field associates a Majorana zero mode with each vison excitation. The vison accompanied by a Majorana zero mode is known to behave as a non-Abelian anyon, which has garnered significant attention for its potential applications in topological quantum computing. Although spatial and temporal control of these anyons is essential for exploring their applicability in quantum computing, numerical simulations of creating, moving, and annihilating anyons by an external field remain challenging as this field violates the exact solvability of the Kitaev model. Moreover, such a field to control anyons may disturb the quantum state due to the energy injection it causes. In this study, by introducing energy dissipation phenomenologically in real-time simulations, we demonstrate that the generation, movement, and annihilation of vison excitations can be achieved while maintaining their localization. We find that a vison can be moved in a desired direction by using time-dependent local magnetic fields or gradient fields, and it remains accompanied by a Majorana zero mode even after its movement. We also reveal that a larger spatial extent of the Majorana zero modes bound to a vison facilitates the movement of the vison with smaller field gradients. Furthermore, our numerical simulations demonstrate pair creation and annihilation of visons, triggered by time-dependent magnetic fields. The results obtained in this study highlight the significance of energy dissipation in controlling non-Abelian anyons, which will stimulate further investigations into the nonequilibrium dynamics of fractional quasiparticles in strongly correlated electron systems, as well as studies for applications in quantum computation. △ Less

Submitted 23 August, 2024; originally announced August 2024.

Comments: 20 pages, 12 figures

Journal ref: Phys. Rev. B 110, 214426 (2024)

A review on magnetic field induced spin crossover in LaCoO$_{3}$ up to 600 T

Authors: Akihiko Ikeda, Yasuhiro H. Matsuda, Keisuke Sato, Joji Nasu

Abstract: \lco{} is known for its two-step spin crossover as a function of temperature. Despite efforts spanning over half a century, the origin of this phenomenon is still debated, particularly regarding how the microscopic spin states are involved in the observed macroscopic two-step spin crossover. High magnetic field studies on LaCoO$_{3}$ are performed because the magnetic field-induced spin crossover… ▽ More \lco{} is known for its two-step spin crossover as a function of temperature. Despite efforts spanning over half a century, the origin of this phenomenon is still debated, particularly regarding how the microscopic spin states are involved in the observed macroscopic two-step spin crossover. High magnetic field studies on LaCoO$_{3}$ are performed because the magnetic field-induced spin crossover is induced, where the magnetic excited states become more stable in high magnetic fields than the non-magnetic ground states. This review focuses on the findings in LaCoO$_{3}$ at high magnetic fields over the last decade. A complex phase diagram has been revealed at high magnetic fields instead of solving the conventional problem of LaCoO$_{3}$. It suggests that appreciable spin state correlations are in play in LaCoO$_{3}$. The possibility of exciton condensation is also discussed. △ Less

Submitted 30 June, 2024; originally announced July 2024.

Comments: A review paper for a special topics in Journal of Physical Society of Japan

Journal ref: J. Phys. Soc. Jpn., 93, 121005 (2024)

Thermal Hall effect incorporating magnon damping in localized spin systems

Authors: Shinnosuke Koyama, Joji Nasu

Abstract: We propose a theory for thermal Hall transport mediated by magnons to address the impact of their damping resulting from magnon-magnon interactions in insulating magnets. This phenomenon is anticipated to be particularly significant in systems characterized by strong quantum fluctuations, exemplified by spin-1/2 systems. Employing a nonlinear flavor-wave theory, we analyze a general model for loca… ▽ More We propose a theory for thermal Hall transport mediated by magnons to address the impact of their damping resulting from magnon-magnon interactions in insulating magnets. This phenomenon is anticipated to be particularly significant in systems characterized by strong quantum fluctuations, exemplified by spin-1/2 systems. Employing a nonlinear flavor-wave theory, we analyze a general model for localized electron systems and develop a formulation for thermal conductivity based on a perturbation theory, utilizing bosonic Green's functions with a nonzero self-energy. We derive the expression of the thermal Hall conductivity incorporating magnon damping. To demonstrate the applicability of the obtained representation, we adopt it to two $S=1/2$ quantum spin models on a honeycomb lattice. In calculations for these systems, we make use of the self-consistent imaginary Dyson equation approach at finite temperatures for evaluating the magnon damping rate. In both systems, the thermal Hall conductivity is diminished due to the introduction of magnon damping over a wide temperature range. This effect arises due to the smearing of magnon spectra with nonzero Berry curvatures. We also discuss the relation to the damping of chiral edge modes of magnons. Our formulation can be applied to various localized electron systems as we begin with a general Hamiltonian for these systems. Our findings shed light on a new aspect of topological magnonics emergent from many-body effects and will stimulate further investigations on the impact of magnon damping on topological phenomena. △ Less

Submitted 13 March, 2024; originally announced March 2024.

Comments: 24 pages, 10 figures

Journal ref: Phys. Rev. B 109, 174442 (2024)

Spin Seebeck Effect as a Probe for Majorana Fermions in Kitaev Spin Liquids

Authors: Yasuyuki Kato, Joji Nasu, Masahiro Sato, Tsuyoshi Okubo, Takahiro Misawa, Yukitoshi Motome

Abstract: Quantum entanglement in strongly correlated electron systems often leads to exotic elementary excitations. Quantum spin liquids (QSLs) provide a paradigmatic example, where the elementary excitations are described by fractional quasiparticles such as spinons. However, such fractional quasiparticles behave differently from electrons, making their experimental identification challenging. Here, we th… ▽ More Quantum entanglement in strongly correlated electron systems often leads to exotic elementary excitations. Quantum spin liquids (QSLs) provide a paradigmatic example, where the elementary excitations are described by fractional quasiparticles such as spinons. However, such fractional quasiparticles behave differently from electrons, making their experimental identification challenging. Here, we theoretically investigate the spin Seebeck effect, which is a thermoelectric response via a spin current, as an efficient probe of the fractional quasiparticles in QSLs, focusing on the Kitaev honeycomb model. By comprehensive studies using the real-time dynamics, the perturbation theory, and the linear spin-wave theory based on the tunnel spin-current theory, we find that the spin current is induced by thermal gradient in the Kitaev spin liquid, via the low-energy fractional Majorana excitations. This underscores the ability of Majorana fermions to carry spin current, despite lacking spin angular momentum. Furthermore, we find that the induced spin current changes its sign depending on the sign of the Kitaev interaction, indicating that the Majorana fermions contribute to the spin current with (up-)down-spin like nature when the exchange coupling is (anti)ferromagnetic. Thus, in contrast to the negative spin current already found in a one-dimensional QSL, our finding reveals that the spin Seebeck effect can exhibit either positive or negative signals, contingent upon the nature of fractional excitations in the QSLs. We also clarify contrasting field-angle dependence between the Kitaev spin liquid in the low-field limit and the high-field ferromagnetic state, which is useful for the experimental identification. Our finding suggests that the spin Seebeck effect could be used not only to detect fractional quasiparticles emerging in QSLs but also to generate and control them. △ Less

Submitted 7 March, 2025; v1 submitted 23 January, 2024; originally announced January 2024.

Comments: 18 pages, 10 figures

Journal ref: Phys. Rev. X 15, 011050 (2025)

Effects of magnetic fields and orbital angular momentum on excitonic condensation in two-orbital Hubbard model

Authors: Ryota Koga, Joji Nasu

Abstract: We investigate the magnetic-field effects on a two-orbital Hubbard model that describes multiple spin states. Cobalt oxides have been investigated as materials possessing spin-state degrees of freedom due to the interplay between the Hund coupling interaction and crystalline field effect. In the competing region, quantum hybridizations between distinct spin states are expected to emerge, correspon… ▽ More We investigate the magnetic-field effects on a two-orbital Hubbard model that describes multiple spin states. Cobalt oxides have been investigated as materials possessing spin-state degrees of freedom due to the interplay between the Hund coupling interaction and crystalline field effect. In the competing region, quantum hybridizations between distinct spin states are expected to emerge, corresponding to excitonic condensation. Applied magnetic fields could also induce such a competition. To understand magnetic-field effects on excitonic condensation in multi-orbital systems, it is crucial to account for contributions from both spin and orbital degrees of freedom to magnetic properties. Here, we study field-induced phenomena in the two-orbital Hubbard model by focusing on the role of the orbital angular momentum. We comprehensively analyze this model on a square lattice employing the Hartree-Fock approximation. Omitting contributions from the orbital moment, we find that an applied magnetic field gives rise to two excitonic phases, besides the spin-state ordered phase, between the nonmagnetic low-spin and spin-polarized high-spin phases. One of these excitonic phases manifests a staggered-type spin-state order, interpreted as an excitonic supersolid state. Conversely, the other phase is not accompanied by it and exhibits only a spin polarization due to the applied magnetic field. When spin-orbit coupling is present, this phase displays a ferrimagnetic spin alignment attributed to spin anisotropy. Our analysis also reveals that incorporating the contribution of the orbital magnetic moment to the Zeeman term significantly alters the overall structure of the phase diagram. Notably, the orbital magnetization destabilizes the excitonic phase in contrast to scenarios without this contribution. We also discuss the relevance of our findings to real materials, such as cobalt oxides. △ Less

Submitted 22 November, 2023; originally announced November 2023.

Comments: 12 pages, 11 figures

Journal ref: J. Phys. Soc. Jpn. 93, 054703 (2024)

Flavor-wave theory with quasiparticle damping at finite temperatures: Application to chiral edge modes in the Kitaev model

Authors: Shinnosuke Koyama, Joji Nasu

Abstract: We propose a theoretical framework to investigate elementary excitations at finite temperatures within a localized electron model that describes the interactions between multiple degrees of freedom, such as quantum spin models and Kugel-Khomskii models. Thus far, their excitation structures have been mainly examined using the linear flavor-wave theory, an SU($N$) generalization of the linear spin-… ▽ More We propose a theoretical framework to investigate elementary excitations at finite temperatures within a localized electron model that describes the interactions between multiple degrees of freedom, such as quantum spin models and Kugel-Khomskii models. Thus far, their excitation structures have been mainly examined using the linear flavor-wave theory, an SU($N$) generalization of the linear spin-wave theory. These techniques introduce noninteracting bosonic quasiparticles as elementary excitations from the ground state, thereby elucidating numerous physical phenomena, including excitation spectra and transport properties characterized by topologically nontrivial band structures. Nevertheless, the interactions between quasiparticles cannot be ignored in systems exemplified by $S=1/2$ quantum spin models, where strong quantum fluctuations are present. Recent studies have investigated the effects of quasiparticle damping at zero temperature in such models. In our study, extending this approach to the flavor-wave theory for general localized electron models, we construct a comprehensive method to calculate excitation spectra with the quasiparticle damping at finite temperatures. We apply our method to the Kitaev model under magnetic fields, a typical example of models with topologically nontrivial magnon bands. Our calculations reveal that chiral edge modes undergo significant damping in weak magnetic fields, amplifying the damping rate by the temperature increase. This effect is caused by collisions with thermally excited quasiparticles. Since our approach starts from a general Hamiltonian, it will be widely applicable to other localized systems, such as spin-orbital coupled systems derived from multi-orbital Hubbard models in the strong correlation limit. △ Less

Submitted 3 August, 2023; originally announced August 2023.

Comments: 19 pages, 10 figures

Journal ref: Phys. Rev. B 108, 235162 (2023)

Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet $α$-RuCl$_3$

Authors: K. Imamura, S. Suetsugu, Y. Mizukami, Y. Yoshida, K. Hashimoto, K. Ohtsuka, Y. Kasahara, N. Kurita, H. Tanaka, P. Noh, J. Nasu, E. -G. Moon, Y. Matsuda, T. Shibauchi

Abstract: The field-induced quantum disordered state of layered honeycomb magnet $α$-RuCl$_3$ is a prime candidate for Kitaev spin liquids hosting Majorana fermions and non-Abelian anyons. Recent observations of anomalous planar thermal Hall effect demonstrate a topological edge mode, but whether it originates from Majorana fermions or bosonic magnons remains controversial. Here we distinguish these origins… ▽ More The field-induced quantum disordered state of layered honeycomb magnet $α$-RuCl$_3$ is a prime candidate for Kitaev spin liquids hosting Majorana fermions and non-Abelian anyons. Recent observations of anomalous planar thermal Hall effect demonstrate a topological edge mode, but whether it originates from Majorana fermions or bosonic magnons remains controversial. Here we distinguish these origins from low-temperature measurements of high-resolution specific heat and thermal Hall conductivity with rotating in-plane fields. In the honeycomb bond direction, a distinct closure of the low-energy bulk gap is observed concomitantly with the sign reversal of the Hall effect. General discussions of topological bands show that this is the hallmark of an angle-rotation-induced topological transition of fermions, providing conclusive evidence for the Majorana-fermion origin of the thermal Hall effect in $α$-RuCl$_3$. △ Less

Submitted 17 May, 2023; originally announced May 2023.

Comments: 21 pages, 7 figures

Journal ref: Sci. Adv. 10, eadk3539 (2024)

Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid

Authors: Chihiro Harada, Atsushi Ono, Joji Nasu

Abstract: The Kitaev quantum spin liquid possesses two fractional quasiparticles, itinerant Majorana fermions and localized visons. It provides a promising platform for realizing a Majorana zero mode trapped by a vison excitation. This local mode behaves as a non-Abelian anyon capable of applications to quantum computation. However, creating, observing, and manipulating visons remain challenging even in the… ▽ More The Kitaev quantum spin liquid possesses two fractional quasiparticles, itinerant Majorana fermions and localized visons. It provides a promising platform for realizing a Majorana zero mode trapped by a vison excitation. This local mode behaves as a non-Abelian anyon capable of applications to quantum computation. However, creating, observing, and manipulating visons remain challenging even in the pristine Kitaev model. Here, we propose a theory to control visons enabled by a time-dependent local magnetic field in the Kitaev spin liquid. Examining the time evolution of the magnetic state, we demonstrate that a vison follows a locally applied field sweeping in the system. We clarify that one can move a vison accompanied by a Majorana zero mode by choosing the velocity and shape of the local field appropriately. In particular, the controllability of visons using local fields shows nonlinear behavior for its strength, which originates from interactions between Majorana fermions and visons. The present results suggest that itinerant Majorana fermions other than zero modes play a crucial role in vison transport. Our finding will offer a guideline for controlling Majorana zero modes in the Kitaev quantum spin liquid. △ Less

Submitted 21 December, 2023; v1 submitted 15 May, 2023; originally announced May 2023.

Comments: 11 pages, 8 figures

Interedge spin resonance in the Kitaev quantum spin liquid

Authors: Takahiro Misawa, Joji Nasu, Yukitoshi Motome

Abstract: The Kitaev model offers a platform for quantum spin liquids (QSLs) with fractional excitations, itinerant Majorana fermions and localized fluxes. Since these fractional excitations could be utilized for quantum computing, how to create, observe, and control them through the spin degree of freedom is a central issue. Here, we study dynamical spin transport in a wide range of frequency for the Kitae… ▽ More The Kitaev model offers a platform for quantum spin liquids (QSLs) with fractional excitations, itinerant Majorana fermions and localized fluxes. Since these fractional excitations could be utilized for quantum computing, how to create, observe, and control them through the spin degree of freedom is a central issue. Here, we study dynamical spin transport in a wide range of frequency for the Kitaev-Heisenberg model, by applying an AC magnetic field to an edge of the system. We find that, in the Kitaev QSL phase, spin polarizations at the other edge are resonantly induced in a specific spin component, even though the static spin correlations are vanishingly small. This interedge spin resonance appears around the input frequency over the broad frequency range. Comparing with the dynamical spin correlations, we clarify that the resonance is governed by the itinerant Majorana fermions with a broad continuum excitation spectrum, which can propagate over long distances, although it vanishes for the pure Kitaev model because of accidental degeneracy and requires weak Heisenberg interactions. We also find that the spin polarizations in the other spin components are weakly induced at an almost constant frequency close to the excitation gap of the localized fluxes, irrespective of the input frequency. These results demonstrate that the dynamical spin transport is a powerful probe of the fractional excitations in the Kitaev QSL. Possible experimental realization of the interedge spin resonance is discussed. △ Less

Submitted 7 September, 2023; v1 submitted 2 April, 2023; originally announced April 2023.

Comments: 12 pages, 9 figure

Journal ref: Phys. Rev. B 108, 115117 (2023)

Field-direction Dependence of Majorana-mediated Spin Transport

Authors: H. Taguchi, A. Koga, Y. Murakami, J. Nasu, H. Tsuchiura

Abstract: We study the field-direction dependence of the Majorana-mediated spin transport in the Kitaev clusters with zigzag and armchair edges, applying a static magnetic field to one of the edges and a magnetic pulsed field to the other edges. By means of the exact diagonalization method, we calculate the time-evolution of the spin moments in both edge regions to clarify how the directions of two fields a… ▽ More We study the field-direction dependence of the Majorana-mediated spin transport in the Kitaev clusters with zigzag and armchair edges, applying a static magnetic field to one of the edges and a magnetic pulsed field to the other edges. By means of the exact diagonalization method, we calculate the time-evolution of the spin moments in both edge regions to clarify how the directions of two fields and shape of the edges affect the Majorana-mediated spin transport. △ Less

Submitted 16 September, 2022; originally announced September 2022.

Comments: 6 pages, 3 figures, to be published in JPS Conference Proceedings (LT29)

Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models

Authors: Kiyu Fukui, Yasuyuki Kato, Joji Nasu, Yukitoshi Motome

Abstract: The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin $S=1/2$ moments on a honeycomb lattice. In recent years, the model has been extended to higher $S$ from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general $S$, especially in the presence of other additional inte… ▽ More The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin $S=1/2$ moments on a honeycomb lattice. In recent years, the model has been extended to higher $S$ from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general $S$, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-$S$ Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general $S$. We show that, similar to the $S=1/2$ case, the phase diagram for higher $S$ contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing $S$, becoming vanishingly narrow for $S\geq 2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search of higher-$S$ Kitaev materials. △ Less

Submitted 8 July, 2022; originally announced July 2022.

Comments: 14 pages, 12 figures

Scattering phenomena for spin transport in Kitaev spin liquid

Authors: Joji Nasu, Yuta Murakami, Akihisa Koga

Abstract: The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, itinerant Majorana fermion and localized flux excitation. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. Here, we focus on spin transport in the presence of excited fluxes and report… ▽ More The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, itinerant Majorana fermion and localized flux excitation. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. Here, we focus on spin transport in the presence of excited fluxes and report that they yield strong interference in the propagation of the Majorana fermions, which feel gauge-like potential emergent around the fluxes. We examine the transient spin dynamics triggered by a pulsed magnetic field at an edge. In the absence of excited fluxes, the magnetic-field pulse creates the plane wave of the Majorana fermions, which flows in the quantum spin liquid. Although this wave does not accompany the change of local spin moments in bulk, it induces local moments at the side opposite to the edge under the magnetic-field pulse. We observe the spatial modulation of induced spin moments when fluxes are excited in the bulk region. This behavior is more striking than the case of lattice defects. Moreover, we find that, although the amplitude of the spatial change is almost independent of the distance between lattice defects, it is strongly enhanced by increasing the distance for the case of excited fluxes. The difference is understood from the influence on the itinerant Majorana fermions; the lattice defects change the system locally, but flux excitations alter all the transfer integrals on the string connecting them. The present results will provide another route to observing intrinsic flux excitations distinguished from extrinsic effects such as lattice defects. △ Less

Submitted 25 April, 2022; originally announced April 2022.

Comments: 15 pages, 10 figures

Feasibility of Kitaev quantum spin liquids in ultracold polar molecules

Authors: Kiyu Fukui, Yasuyuki Kato, Joji Nasu, Yukitoshi Motome

Abstract: Ultracold atoms and molecules trapped in optical lattices are expected to serve as simulators of strongly correlated systems and topological states of matter. A fascinating example is to realize the Kitaev quantum spin liquid by using ultracold polar molecules. However, although experimental implementation of the Kitaev-type interaction was proposed, the stability of the Kitaev quantum spin liquid… ▽ More Ultracold atoms and molecules trapped in optical lattices are expected to serve as simulators of strongly correlated systems and topological states of matter. A fascinating example is to realize the Kitaev quantum spin liquid by using ultracold polar molecules. However, although experimental implementation of the Kitaev-type interaction was proposed, the stability of the Kitaev quantum spin liquid has not been fully investigated thus far. Here we study a quantum spin model with long-range angle-dependent Kitaev-type interactions proposed for the polar molecules, by the pseudofermion functional renormalization group method. We reveal that the ground state is magnetically ordered in both ferromagnetic and antiferromagnetic models regardless of the spatial anisotropy of the interactions, while the isotropic case is most frustrated and closest to the realization of the Kitaev quantum spin liquid. Furthermore, by introducing a cutoff in the interaction range, we clarify how the Kitaev quantum spin liquid is destroyed by the long-range interactions. The results urge us to reconsider the feasibility of the Kitaev quantum spin liquid in ultracold polar molecules. △ Less

Submitted 12 April, 2022; originally announced April 2022.

Comments: 13 pages, 13 figures

Journal ref: Phys. Rev. B 106, 014419 (2022)

Evidence for the first-order topological phase transition in a Kitaev spin liquid candidate $α$-RuCl$ _3$

Authors: S. Suetsugu, Y. Ukai, M. Shimomura, M. Kamimura, T. Asaba, Y. Kasahara, N. Kurita, H. Tanaka, T. Shibauchi, J. Nasu, Y. Motome, Y. Matsuda

Abstract: The Kitaev quantum spin liquid (QSL) on the two-dimensional honeycomb lattice epitomizes an entangled topological state, where the spins fractionalize into Majorana fermions. This state has aroused tremendous interest because it harbors non-Abelian anyon excitations. The half-integer quantized thermal Hall (HIQTH) conductance observed in $α$-RuCl$_3$ is a key signature of these excitations. Howeve… ▽ More The Kitaev quantum spin liquid (QSL) on the two-dimensional honeycomb lattice epitomizes an entangled topological state, where the spins fractionalize into Majorana fermions. This state has aroused tremendous interest because it harbors non-Abelian anyon excitations. The half-integer quantized thermal Hall (HIQTH) conductance observed in $α$-RuCl$_3$ is a key signature of these excitations. However, the fate of this topologically nontrivial state at intense fields remains largely elusive. Here, we report the thermal conductivity $κ$ and specific heat $C$ of $α$-RuCl$_3$ with in-plane magnetic fields $H$. For the field direction perpendicular to the Ru-Ru bond, where the HIQTH effect is observed, we find a discontinuous jump in $κ(H)$ and a peak anomaly in $C(H)$ at $μ_0H^*\approx11$\,T, evidencing a weak first-order phase transition. Remarkably, the HIQTH effect vanishes close to $H^*$. Furthermore, we find that the spin-fractionalization feature is retained well above $H^\ast$. These imply the emergence of the phase transition that separates two QSL phases with distinct topological properties. △ Less

Submitted 1 March, 2022; originally announced March 2022.

Comments: 6 pages, 4 figures

Journal ref: J. Phys. Soc. Jpn. 91, 124703 (2022)

Signature of spin-triplet exciton condensations in LaCoO$_{3}$ at ultrahigh magnetic fields up to 600 T

Authors: Akihiko Ikeda, Yasuhiro H. Matsuda, Keisuke Sato, Yuto Ishii, Hironobu Sawabe, Daisuke Nakamura, Shojiro Takeyama, Joji Nasu

Abstract: Bose-Einstein condensation of electron-hole pairs, exciton condensation, has been effortfully investigated since predicted 60 years ago. Irrefutable evidence has still been lacking due to experimental difficulties in verifying the condensation of the charge neutral and non-magnetic spin-singlet excitons. Whilst, condensation of spin-triplet excitons is a promising frontier because spin supercurren… ▽ More Bose-Einstein condensation of electron-hole pairs, exciton condensation, has been effortfully investigated since predicted 60 years ago. Irrefutable evidence has still been lacking due to experimental difficulties in verifying the condensation of the charge neutral and non-magnetic spin-singlet excitons. Whilst, condensation of spin-triplet excitons is a promising frontier because spin supercurrent and spin-Seebeck effects will be observable. A canonical cobaltite LaCoO$_{3}$ under very high magnetic fields is a propitious candidate, yet to be verified. Here, we unveil the exotic phase diagram of LaCoO$_{3}$ up to 600 T generated using the electromagnetic flux compression method and the state-of-the-art magnetostriction gauge. We found the continuous magnetostriction curves and a bending structure, which suggest the emergence of two distinct spin-triplet exciton condensates. By constructing a phenomenological model, we showed that quantum fluctuations of excitons are crucial for the field-induced successive transitions. The spin-triplet exciton condensation in a cobaltite, which is three-dimensional and thermally equilibrated, opens up a novel venue for spintronics technologies with spin-supercurrent such as a spin Josephson junction. △ Less

Submitted 20 March, 2023; v1 submitted 7 January, 2022; originally announced January 2022.

Comments: 6 pages, 4 figures plus supplementary material

Journal ref: Nat. Commun. 14, 1744 (2023)

Antisymmetric Thermopolarization by Electric Toroidicity

Authors: Joji Nasu, Satoru Hayami

Abstract: We investigate electric polarizations emergent perpendicular to an applied thermal gradient in insulating systems. The thermally-induced electric polarization, known as thermopolarization, has been studied conventionally in the case that an electric polarization appears along the thermal gradient. Here, we focus on the antisymmetric component of the thermopolarization tensor and reveal that it bec… ▽ More We investigate electric polarizations emergent perpendicular to an applied thermal gradient in insulating systems. The thermally-induced electric polarization, known as thermopolarization, has been studied conventionally in the case that an electric polarization appears along the thermal gradient. Here, we focus on the antisymmetric component of the thermopolarization tensor and reveal that it becomes nonzero owing to the ferro-type order for electric-toroidal dipole moments. To describe local electric polarizations originating from the disproportionation of localized electronic clouds, we introduce a two-dimensional three-orbital model with localized $s$ and two $p$ orbitals, where the electric polarization at each site interacts with the neighboring one as dipole-dipole interactions. We find that a vortex-type configuration of local electric polarizations appears as a mean-field ground state, corresponding to a ferro-type electric-toroidal dipole order. By taking account of collective modes from this ordered state, we calculate the coefficient of the thermopolarization based on the linear response theory. The antisymmetric component is nonzero in the presence of the electric-toroidal dipole order. We clarify that fluctuations in the $p$ orbitals are crucial in enhancing the antisymmetric thermopolarization. We discuss the appearance conditions based on the symmetry argument and the relevance to real materials. △ Less

Submitted 12 December, 2021; originally announced December 2021.

Comments: 10 pages, 9 figures

Role of Majorana fermions in spin transport of anisotropic Kitaev model

Authors: Hirokazu Taguchi, Yuta Murakami, Akihisa Koga, Joji Nasu

Abstract: We study a quantum spin Kitaev model with zigzag edges to clarify the effects of anisotropy in the exchange couplings on the spin propagation. We simulate the spin and Majorana dynamics triggered by a magnetic pulse, using the real-space time-dependent Majorana mean-field theory. When the anisotropy is small, the dispersion of the itinerant Majorana fermions remains gapless, where the velocity of… ▽ More We study a quantum spin Kitaev model with zigzag edges to clarify the effects of anisotropy in the exchange couplings on the spin propagation. We simulate the spin and Majorana dynamics triggered by a magnetic pulse, using the real-space time-dependent Majorana mean-field theory. When the anisotropy is small, the dispersion of the itinerant Majorana fermions remains gapless, where the velocity of the spin propagation matches the group velocity of the itinerant Majorana fermions at the nodal points. On the other hand, in the gapped system with a large anisotropy, the spin propagation is strongly suppressed although its nature depends on the shape of the pulse. The spin transport in the junction system described by the Kitaev models with distinct anisotropies is also dressed. △ Less

Submitted 9 May, 2021; originally announced May 2021.

Comments: 9 pages, 7 figures

Journal ref: Phys. Rev. B 104, 125139 (2021)

Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system

Authors: Shinnosuke Koyama, Joji Nasu

Abstract: We study magnetic excitations and thermal Hall effect on the Kitaev-Heisenberg model under magnetic fields. By employing the spin-wave theory for the magnetic orders realized in this model, we examine the topological nature of the spin-wave dispersions and calculate the thermal Hall conductivity. The comprehensive investigations on the field-angle dependence clarify that the thermal Hall conductiv… ▽ More We study magnetic excitations and thermal Hall effect on the Kitaev-Heisenberg model under magnetic fields. By employing the spin-wave theory for the magnetic orders realized in this model, we examine the topological nature of the spin-wave dispersions and calculate the thermal Hall conductivity. The comprehensive investigations on the field-angle dependence clarify that the thermal Hall conductivity is sensitive to the spin ordered pattern and excitation spectra of magnons; this quantity is enhanced by the noncoplanar spin configurations and small magnon gap in the excitation spectrum. On the other hand, we also find a common feature in the field-angle dependence of the thermal Hall conductivity. It vanishes when the magnetic field is on the planes spanned by the spin axes. We reveal that the behavior is intrinsic to the Kitaev -Heisenberg model in an applied field and demonstrate that the introduction of the off-diagonal spin interaction causes the disappearance of the feature in the thermal Hall conductivity. △ Less

Submitted 7 May, 2021; originally announced May 2021.

Comments: 12 pages, 10 figures

Journal ref: Phys. Rev. B 104, 075121 (2021)

Spin dynamics in the Kitaev model with disorder: Quantum Monte Carlo study of dynamical spin structure factor, magnetic susceptibility, and NMR relaxation rate

Authors: Joji Nasu, Yukitoshi Motome

Abstract: We investigate the impact of two types of disorder, bond randomness and site dilution, on the spin dynamics in the Kitaev model on a honeycomb lattice. The ground state of this model is a canonical quantum spin liquid with spin fractionalization into two types of quasiparticles, itinerant Majorana fermions and localized fluxes. Using unbiased quantum Monte Carlo simulations, we calculate the tempe… ▽ More We investigate the impact of two types of disorder, bond randomness and site dilution, on the spin dynamics in the Kitaev model on a honeycomb lattice. The ground state of this model is a canonical quantum spin liquid with spin fractionalization into two types of quasiparticles, itinerant Majorana fermions and localized fluxes. Using unbiased quantum Monte Carlo simulations, we calculate the temperature evolution of the dynamical spin structure factor, the magnetic susceptibility, and the NMR relaxation rate. In the dynamical spin structure factor, we find that the two types of disorder affect seriously the low-energy peak dominantly originating from the flux excitations, rather than the high-energy continuum from the Majorana excitations, in a different way: The bond randomness softens the peak to the lower energy with broadening, whereas the site dilution smears the peak and in addition develops the other sharp peaks inside the spin gap including the zero energy. We show that the zero-energy spin excitations, which originate from the Majorana zero modes induced around the site vacancies, survive up to the temperature comparable to the energy scale of the Kitaev interaction. For the bond randomness, the low-temperature susceptibility does not show any qualitative change against the weak disorder, but it changes to divergent behavior while increasing the strength of disorder. Similar distinct behaviors for the weak and strong disorder are observed also in the NMR relaxation rate; an exponential decay changes into a power-law decay. In contrast, for the site dilution, we find no such crossover; divergent behavior in the susceptibility and a power-law decay in the NMR relaxation rate appear immediately with the introduction of the site dilution. We discuss the relevance of our results to experiments for the Kitaev candidate materials with disorders. △ Less

Submitted 21 April, 2021; originally announced April 2021.

Comments: 18 pages, 11 figures

Journal ref: Phys. Rev. B 104, 035116 (2021)

Majorana correlations in the Kitaev model with ordered-flux structures

Authors: Akihisa Koga, Yuta Murakami, Joji Nasu

Abstract: We study the effects of the flux configurations on the emergent Majorana fermions in the $S=1/2$ Kitaev model on a honeycomb lattice, where quantum spins are fractionalized into itinerant Majorana fermions and localized fluxes. A quantum spin liquid appears as the ground state of the Kitaev model in the flux-free sector, which has intensively been investigated so far. In this flux sector, the Majo… ▽ More We study the effects of the flux configurations on the emergent Majorana fermions in the $S=1/2$ Kitaev model on a honeycomb lattice, where quantum spins are fractionalized into itinerant Majorana fermions and localized fluxes. A quantum spin liquid appears as the ground state of the Kitaev model in the flux-free sector, which has intensively been investigated so far. In this flux sector, the Majorana fermion system has linear dispersions and shows power law behavior in the Majorana correlations. On the other hand, periodically-arranged flux configurations yield low-energy excitations in the Majorana fermion system, which are distinctly different from those in the flux-free state. We find that one of the periodically arranged flux states results in the gapped Majorana dispersion and the exponential decay in the Majorana correlations. The Kitaev system with another flux configuration exhibits a semi-Dirac like dispersion, leading to the power law decay with a smaller power than that in the flux-free sector along symmetry axes. We also examine the effect of the randomness in the flux configurations and clarify that the Majorana density of states is filled by increasing the flux density, and power-law decay in the Majorana correlations remains. The present results could be important to control the motion of Majorana fermions, which carries the spin excitations, in the Kitaev candidate materials. △ Less

Submitted 5 April, 2021; originally announced April 2021.

Comments: 9 pages, 14 figures

Journal ref: Phys. Rev. B 103, 214421 (2021)

Spin Seebeck Effect in Nonmagnetic Excitonic Insulators

Authors: Joji Nasu, Makoto Naka

Abstract: We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneous… ▽ More We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state without magnetic fields. The spin Seebeck effect originates from spin-split collective excitation modes although the ground state does not exhibit any magnetic orderings. This peculiar phenomenon is inherent in the excitonic insulating state, whose order parameter is time-reversal odd and yields a spin splitting for the collective excitation modes. We also find that the spin current is strongly enhanced and its direction is inverted in the vicinity of the phase transition to another magnetically ordered phase. We suggest that the present phenomenon is possibly observed in perovskite cobaltites with the GdFeO$_3$-type lattice distortion. △ Less

Submitted 29 November, 2020; originally announced November 2020.

Comments: 16 pages, 4 figures

Journal ref: Phys. Rev. B 103, 121104 (2021)

Strong enhancement of magnetic susceptibility induced by spin-nematic fluctuations in an excitonic insulating system with spin-orbit coupling

Authors: Joji Nasu, Makoto Naka, Sumio Ishihara

Abstract: Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton condensation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theor… ▽ More Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton condensation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the magnetic moment appears in the EI state, which is continuously connected to the forced ferromagnetic state. On the other hand, in the presence of the SOC, they are separated by a phase boundary. We find that the magnetic susceptibility is strongly enhanced in the EI phase near the boundary with a small SOC. This peculiar behavior is attributed to the low-energy fluctuation of the spin nematicity inherent in the high-spin local state stabilized by the Hund coupling. The present study not only reveals the impact of the SOC for the EI state but also sheds light on the role of quantum fluctuations of the spin nematicity for the EI state. △ Less

Submitted 7 May, 2020; originally announced May 2020.

Comments: 9 pages, 8 figures

Journal ref: Phys. Rev. B 102, 045143 (2020)

Thermodynamic and Transport Properties in Disordered Kitaev Models

Authors: Joji Nasu, Yukitoshi Motome

Abstract: Effects of bond randomness and site dilution are systematically investigated for the Kitaev model describing a quantum spin liquid with fractional excitations of itinerant Majorana fermions and localized fluxes. We find that, in the high-temperature region where the itinerant Majorana fermions release their entropy, both types of disorders suppress the longitudinal thermal conductivity while keepi… ▽ More Effects of bond randomness and site dilution are systematically investigated for the Kitaev model describing a quantum spin liquid with fractional excitations of itinerant Majorana fermions and localized fluxes. We find that, in the high-temperature region where the itinerant Majorana fermions release their entropy, both types of disorders suppress the longitudinal thermal conductivity while keeping the specific heat almost unchanged. This suggests that both disorders reduce the mean-free path of the Majorana fermions. On the other hand, in the low-temperature region, the other specific heat peak associated with the entropy release from the localized fluxes is suppressed for both cases, but it is broadened and shifted to the lower-temperature side by the bond randomness, while the position and the width are almost unchanged against the site dilution. Contrasting behavior is also found in the thermal Hall effect under a magnetic field; the half quantization of the thermal Hall conductivity is fragile against the site dilution, while it remains for the bond randomness despite the reduced onset temperature. We discuss the contrasting behavior from the stability of the topological nature by calculating flux condensation and Majorana excitation gap. △ Less

Submitted 16 April, 2020; originally announced April 2020.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. B 102, 054437 (2020)

The range of non-Kitaev terms and fractional particles in RuCl$_3$

Authors: Yiping Wang, Gavin B. Osterhoudt, Yao Tian, Paige Lampen-Kelley, Arnab Banerjee, Thomas Goldstein, Jun Yan, Johannes Knolle, Huiwen Ji, Robert J. Cava, Joji Nasu, Yukitoshi Motome, Stephen E. Nagler, David Mandrus, Kenneth S. Burch

Abstract: Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size… ▽ More Significant efforts have focused on the magnetic excitations of relativistic Mott insulators, predicted to realize the Kitaev quantum spin liquid (QSL). This exactly solvable model involves a highly entangled state resulting from bond-dependent Ising interactions that produce excitations which are non-local in terms of spin flips. A key challenge in real materials is identifying the relative size of the non-Kitaev terms and their role in the emergence or suppression of fractional excitations. Here, we identify the energy and temperature boundaries of non-Kitaev interactions by direct comparison of the Raman susceptibility of RuCl3 with quantum Monte Carlo (QMC) results for the Kitaev QSLs. Moreover, we further confirm the fractional nature of the magnetic excitations, which is given by creating a pair of fermionic quasiparticles. Interestingly, this fermionic response remains valid in the non-Kitaev range. Our results and focus on the use of the Raman susceptibility provide a stringent new test for future theoretical and experimental studies of QSLs. △ Less

Submitted 18 March, 2020; originally announced March 2020.

Comments: https://www.nature.com/articles/s41535-020-0216-6. arXiv admin note: substantial text overlap with arXiv:1809.07782

Journal ref: npj Quantum Materials (2020) 5:14

Spin transport in the Quantum Spin Liquid State in the $S=1$ Kitaev model: role of the fractionalized quasiparticles

Authors: Akihisa Koga, Tetsuya Minakawa, Yuta Murakami, Joji Nasu

Abstract: We investigate the real-time spin response of the $S=1$ Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is under… ▽ More We investigate the real-time spin response of the $S=1$ Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carry the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations occur in the $S=1$ Kitaev model as well as the exactly solvable $S=1/2$ Kitaev one and the fractionalized quasiparticles play an essential role in the spin transport. △ Less

Submitted 21 January, 2020; originally announced January 2020.

Comments: 5 pages, 5 figures

Journal ref: J. Phys. Soc. Jpn., 89, 033701 (2020)

Half-integer quantized anomalous thermal Hall effect in the Kitaev material $α$-RuCl$_3$

Authors: T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara, T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, C. Hickey, S. Trebst, Y. Matsuda

Abstract: Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $α$-RuCl$_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $α$-RuCl$_3$. Strikingly, the thermal Hall plateau appear… ▽ More Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $α$-RuCl$_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $α$-RuCl$_3$. Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is either $\pm$1, as the Majorana band structure of the pure Kitaev spin liquid. This observation of a half-integer anomalous thermal Hall effect firmly establishes that the Kitaev interaction is primarily responsible and that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in $α$-RuCl$_3$. △ Less

Submitted 7 January, 2020; originally announced January 2020.

Comments: 14 pages, 4 figures

Journal ref: Science 373, 568-572 (2021)

Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids

Authors: Tetsuya Minakawa, Yuta Murakami, Akihisa Koga, Joji Nasu

Abstract: We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with a zigzag structure in terms of the time-dependent Majorana mean-field theory. After the magnetic field pulse is introduced to one of the edges, the spin moments are excited in the opposite edge region although no spin moments are induced in the Kit… ▽ More We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with a zigzag structure in terms of the time-dependent Majorana mean-field theory. After the magnetic field pulse is introduced to one of the edges, the spin moments are excited in the opposite edge region although no spin moments are induced in the Kitaev QSL region. This unusual spin transport originates from the fact that the $S=1/2$ spins are fractionalized into the itinerant and localized Majorana fermions in the Kitaev system. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant Majorana fermions flow through the bulk regime without the spin excitation, resulting in the spin transport in the Kitaev system. We also demonstrate that this phenomenon can be observed even in the system with the Heisenberg interactions using the exact diagonalization. △ Less

Submitted 22 December, 2019; originally announced December 2019.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. Lett. 125, 047204 (2020)

Ferromagnetically ordered metal in the single-band Hubbard model

Authors: Akihisa Koga, Yusuke Kamogawa, Joji Nasu

Abstract: We study a ferromagnetic instability in a single-band Hubbard model on the hypercubic lattice away from half filling. Using dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations based on the segment algorithm, we calculate the magnetic susceptibility in the weak and strong coupling regions systematically. We then find how ferromagnetic fluctuations are enhanced when… ▽ More We study a ferromagnetic instability in a single-band Hubbard model on the hypercubic lattice away from half filling. Using dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations based on the segment algorithm, we calculate the magnetic susceptibility in the weak and strong coupling regions systematically. We then find how ferromagnetic fluctuations are enhanced when the interaction strength and density of holes are varied. The efficiency of the double flip updates in the Monte Carlo simulations is also addressed. △ Less

Submitted 10 December, 2019; originally announced December 2019.

Comments: 4 pages, 2 figures

Magnetic properties of the S = 1 Kitaev model with anisotropic interactions

Authors: Tetsuya Minakawa, Joji Nasu, Akihisa Koga

Abstract: We investigate magnetic properties in the $S=1$ Kitaev model in the anisotropic limit. Performing the fourth-order perturbation expansion with respect to the $x$-bonds, $y$-bonds, and magnetic field, we derive the effective Hamiltonian, where the low-energy physics should be described by the free spins with an effective magnetic field. Making use of the exact diagonalization method for small clust… ▽ More We investigate magnetic properties in the $S=1$ Kitaev model in the anisotropic limit. Performing the fourth-order perturbation expansion with respect to the $x$-bonds, $y$-bonds, and magnetic field, we derive the effective Hamiltonian, where the low-energy physics should be described by the free spins with an effective magnetic field. Making use of the exact diagonalization method for small clusters, we discuss ground-state properties in the system complementary. △ Less

Submitted 23 September, 2019; originally announced September 2019.

Comments: 6 pages, 4 figures

Hunting Majorana Fermions in Kitaev Magnets

Authors: Yukitoshi Motome, Joji Nasu

Abstract: A Majorana fermion is a fermionic particle that is its own antiparticle. Since the theoretical discovery in 1937, the exotic particle has long been searched in particle physics. In the last few decades, however, it has attracted renewed interest in condensed matter physics, where it can be realized as an elementary excitation (quasiparticle) in quantum states of matter. In this review, we discuss… ▽ More A Majorana fermion is a fermionic particle that is its own antiparticle. Since the theoretical discovery in 1937, the exotic particle has long been searched in particle physics. In the last few decades, however, it has attracted renewed interest in condensed matter physics, where it can be realized as an elementary excitation (quasiparticle) in quantum states of matter. In this review, we discuss another platform for Majorana fermions, the quantum spin liquid, in which interacting magnetic moments remain disordered down to the lowest temperature under strong quantum fluctuations. They are characterized by topological entanglement and fractional excitations, whose possible application to topological quantum computation is recently discussed intensively. As a prime candidate for such exotic states, we here focus on the Kitaev magnets, a subgroup of the spin-orbit Mott insulators. After a brief overview of the Kitaev model and the fractionalization of spins in the exact ground state, we review recent explosive development in this rapidly growing field, with a focus on numerical solutions of the Kitaev model at finite temperatures and the comparison with experiments. The key concept is thermal fractionalization --- two types of fractional excitations manifest themselves at largely different temperatures. This leads to distinct thermodynamics and spin dynamics in a variety of experimentally measurable quantities. We discuss such peculiar behaviors as the signatures of fractional quasiparticles, in careful comparison with the available experimental data for the candidate materials of the Kitaev magnets. Our review gives an overview of the current status of the identification of Majorana fermions in the Kitaev magnets, which would serve as a basis for further experimental and theoretical studies toward the manipulation of the exotic particles for topological quantum computation. △ Less

Submitted 12 November, 2019; v1 submitted 5 September, 2019; originally announced September 2019.

Comments: 41 pages, 47 figures, accepted for publication in JPSJ as an invited review paper

Journal ref: J. Phys. Soc. Jpn. 89, 012002 (2020)

Majorana-Magnon Crossover by a Magnetic Field in the Kitaev Model: Continuous-Time Quantum Monte Carlo Study

Authors: Junki Yoshitake, Joji Nasu, Yasuyuki Kato, Yukitoshi Motome

Abstract: Kitaev quantum spin liquids host Majorana fermions via the fractionalization of spins. In a magnetic field, the Majorana fermions were predicted to comprise a topological state, which has attracted great attention by the discovery of the half-quantized thermal Hall conductivity. Nevertheless, a reliable theory remains elusive for the field effect, especially at finite temperature. Here we present… ▽ More Kitaev quantum spin liquids host Majorana fermions via the fractionalization of spins. In a magnetic field, the Majorana fermions were predicted to comprise a topological state, which has attracted great attention by the discovery of the half-quantized thermal Hall conductivity. Nevertheless, a reliable theory remains elusive for the field effect, especially at finite temperature. Here we present unbiased large-scale numerical results for the Kitaev model in a wide range of magnetic field and temperature. We find that the unconventional paramagnetic region showing fractional spin dynamics extends at finite temperature, far beyond the field range where the topological state is expected at zero temperature. Our results show the confinement-deconfinement behavior between the fractional Majorana excitations and the conventional magnons. △ Less

Submitted 11 March, 2020; v1 submitted 16 July, 2019; originally announced July 2019.

Comments: 6 pages, 4 figures, accepter for the publication in Physical Review B: Rapid Communications

Journal ref: Phys. Rev. B 101, 100408 (2020)

Residual Entropy and Spin Fractionalizations in the Mixed-Spin Kitaev Model

Authors: Akihisa Koga, Joji Nasu

Abstract: We investigate ground-state and finite temperature properties of the mixed-spin $(s, S)$ Kitaev model. When one of spins is half-integer and the other is integer, we introduce two kinds of local symmetries, which results in a macroscopic degeneracy in each energy level. Applying the exact diagonalization to several clusters with $(s, S)=(1/2, 1)$, we confirm the presence of this large degeneracy i… ▽ More We investigate ground-state and finite temperature properties of the mixed-spin $(s, S)$ Kitaev model. When one of spins is half-integer and the other is integer, we introduce two kinds of local symmetries, which results in a macroscopic degeneracy in each energy level. Applying the exact diagonalization to several clusters with $(s, S)=(1/2, 1)$, we confirm the presence of this large degeneracy in the ground states, in contrast to the conventional Kitaev models. By means of the thermal pure quantum state technique, we calculate the specific heat, entropy, and spin-spin correlations in the system. We find that in the mixed-spin Kitaev model with $(s, S)=(1/2, 1)$, at least, the double peak structure appears in the specific heat and the plateau in the entropy at intermediate temperatures, indicating the existence of the spin fractionalization. Deducing the entropy in the mixed-spin system with $s, S\le 2$ systematically, we clarify that the smaller spin-$s$ is responsible for the thermodynamic properties at higher temperatures. △ Less

Submitted 10 June, 2019; originally announced June 2019.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. B 100, 100404 (2019)

Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids

Authors: Joji Nasu, Yukitoshi Motome

Abstract: The honeycomb Kitaev spin model provides a quantum spin liquid in the ground state, where the spin excitations are fractionalized into itinerant and localized Majorana fermions; the former spectrum has a broad continuum ranging up to a high energy, while the latter has a sharp peak at a low energy. Despite tremendous efforts, it remains elusive to clearly identify these distinct Majorana excitatio… ▽ More The honeycomb Kitaev spin model provides a quantum spin liquid in the ground state, where the spin excitations are fractionalized into itinerant and localized Majorana fermions; the former spectrum has a broad continuum ranging up to a high energy, while the latter has a sharp peak at a low energy. Despite tremendous efforts, it remains elusive to clearly identify these distinct Majorana excitations in experiments. Here we show their manifestation in the time evolution after quenching the magnetic field, by using the time-dependent Majorana mean-field theory for both the ferromagnetic and antiferromagnetic Kitaev models. We find that the transient spin dynamics from the quantum spin liquid states is qualitatively different from the conventional spin precessions by the quench from the high-field forced-ferromagnetic state. We obtain peculiar time evolutions with distinct time scales, i.e., short-time decay of high-energy components associated with the itinerant Majorana excitations, and long-lived excitations at a low energy by the localized ones. These peculiar behaviors are caused by the energy transfer between the two Majorana quasiparticles after the field quench. Moreover, we find that the Majorana semimetal with the point nodes in equilibrium turns into a Majorana metal with the transient "Fermi surfaces" by the energy transfer. In particular, for the quench from the intermediate-field quantum spin liquid in the antiferromagnetic Kitaev model, the Fermi surfaces change their topology in the time evolution, which is regarded as a dynamical version of the Majorana "Lifshitz transition". Our results unveil that the real-time dynamics provides another route to not only the identification of the fractional Majorana excitations in candidate materials of Kitaev magnets but also unprecedented quantum phases that cannot be stabilized as the equilibrium states. △ Less

Submitted 27 May, 2019; originally announced May 2019.

Comments: 16 pages, 13 figures

Journal ref: Phys. Rev. Research 1, 033007 (2019)

Ferromagnetic Instability for single-band Hubbard model in the strong-coupling regime

Authors: Yusuke Kamogawa, Joji Nasu, Akihisa Koga

Abstract: We study a ferromagnetic instability in a doped single-band Hubbard model by means of dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations. Examining the effect of the strong correlations in the system on the hypercubic and Bethe lattice, we find that the ferromagnetically ordered state appears in the former, while it does not in the latter. We also reveal that the… ▽ More We study a ferromagnetic instability in a doped single-band Hubbard model by means of dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations. Examining the effect of the strong correlations in the system on the hypercubic and Bethe lattice, we find that the ferromagnetically ordered state appears in the former, while it does not in the latter. We also reveal that the ferromagnetic order is more stable in the case that the noninteracting DOS exhibits a slower decay in the high-energy region. The present results suggest that, in the strong-coupling regime, the high-energy part of DOS plays an essential role for the emergence of the ferromagnetically ordered state, in contrast to the Stoner criterion justified in the weak interaction limit. △ Less

Submitted 2 April, 2019; originally announced April 2019.

Comments: 6 pages, 9 figures

Journal ref: Phys. Rev. B 99, 235107 (2019)

Low temperature properties in the Bilayer Kitaev model

Authors: Hiroyuki Tomishige, Joji Nasu, Akihisa Koga

Abstract: The ground state of the bilayer Kitaev model with the Heisenberg-type interlayer exchange interaction is investigated by means of the exact diagonalization. Calculating the ground-state energy, local quantity defined on each plaquette, and dynamical spin structure factor, we obtain results suggesting the existence of a quantum phase transition between the Kitaev quantum spin liquid (QSL) and dimer… ▽ More The ground state of the bilayer Kitaev model with the Heisenberg-type interlayer exchange interaction is investigated by means of the exact diagonalization. Calculating the ground-state energy, local quantity defined on each plaquette, and dynamical spin structure factor, we obtain results suggesting the existence of a quantum phase transition between the Kitaev quantum spin liquid (QSL) and dimer singlet states when the interlayer coupling is antiferromagnetic. On the other hand, increasing the ferromagnetic interlayer coupling, there exists no singularity in the physical quantities, suggesting that the $S=1/2$ Kitaev QSL state realized in each layer adiabatically connects to another QSL state realized in the $S=1$ Kitaev model. Thermodynamic properties are also studied by means of the thermal pure quantum state method. △ Less

Submitted 31 January, 2019; originally announced February 2019.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. B 99, 174424 (2019)

Quasiperiodicity and valence fluctuation in the spin-1/2 Falicov-Kimball model

Authors: Joji Nasu, Ryu Shinzaki, Akihisa Koga

Abstract: We study the spin-1/2 Falicov-Kimball model with conduction and localized $f$ electrons on the Penrose lattice using the real-space dynamical mean-field theory. By changing the $f$ electron level, the $f$ electron density at each site changes continuously, in contrast to periodic systems with first-order valence transitions. In the intermediate valence regime, the local $f$ electron number strongl… ▽ More We study the spin-1/2 Falicov-Kimball model with conduction and localized $f$ electrons on the Penrose lattice using the real-space dynamical mean-field theory. By changing the $f$ electron level, the $f$ electron density at each site changes continuously, in contrast to periodic systems with first-order valence transitions. In the intermediate valence regime, the local $f$ electron number strongly depends on a wider range of the Penrose structure surrounding its lattice site, in spite of the local interaction between the conduction and $f$ electrons. The temperature dependence of the magnetic response is also discussed. △ Less

Submitted 11 December, 2018; originally announced December 2018.

Comments: 7 pages, 5 figures, accepted for publication in Journal of Low Temperature Physics

Staggered ordered phases in the three-orbital Hubbard model

Authors: Kosuke Ishigaki, Joji Nasu, Akihisa Koga, Shintaro Hoshino, Philipp Werner

Abstract: We study ordered phases with broken translational symmetry in the half-filled three-orbital Hubbard model with antiferromagnetic Hund coupling by means of dynamical mean-field theory (DMFT) and continuous-time quantum Monte Carlo simulations. The stability regions of the antiferro-orbital (AFO), antiferro-magnetic (AFM), and charge density wave (CDW) states are determined by measuring the correspo… ▽ More We study ordered phases with broken translational symmetry in the half-filled three-orbital Hubbard model with antiferromagnetic Hund coupling by means of dynamical mean-field theory (DMFT) and continuous-time quantum Monte Carlo simulations. The stability regions of the antiferro-orbital (AFO), antiferro-magnetic (AFM), and charge density wave (CDW) states are determined by measuring the corresponding order parameters. We introduce two symmetrically distinct AFO order parameters and show that these are the primary order parameters in the phase diagram. The CDW and AFM states appear simultaneously with these two types of AFO orders in the weak and strong coupling region, respectively. The DMFT phase diagram is consistent with the results obtained by the Hartree approximation and strong-coupling perturbation theory. In the weak coupling regime, a nontrivial exponent $β=3/2$ is found for the CDW order parameter, which is related to the coupling between the CDW and AFO orders in the Landau theory characteristic for the three-orbital model. We also demonstrate the existence of a metallic AFO state without any charge disproportions and magnetic orders, which appears only at finite temperatures. △ Less

Submitted 29 November, 2018; originally announced November 2018.

Comments: 11 pages, 13 figures

Journal ref: Phys. Rev. B 99, 085131 (2019)

Quantum and classical behavior of spin-$S$ Kitaev models in an anisotropic limit

Authors: Tetsuya Minakawa, Joji Nasu, Akihisa Koga

Abstract: We study low-energy properties of spin-$S$ Kitaev models in an anisotropic limit. The effective form of a local conserved quantity is derived in the low-energy subspace. We find this is the same as that of $S=1/2$ case for the half-integer spins but shows a different form for the integer spins. Applying the perturbation theory to the anisotropic Kitaev model, we obtain the effective Hamiltonian. I… ▽ More We study low-energy properties of spin-$S$ Kitaev models in an anisotropic limit. The effective form of a local conserved quantity is derived in the low-energy subspace. We find this is the same as that of $S=1/2$ case for the half-integer spins but shows a different form for the integer spins. Applying the perturbation theory to the anisotropic Kitaev model, we obtain the effective Hamiltonian. In the integer spin case, the effective model is equivalent to a free spin model under an uniform magnetic field, where quantum fluctuations are quenched. On the other hand, in the half-integer case, the system is described by the toric code Hamiltonian, where quantum fluctuations play a crucial role in the ground state. The boundary effect in the anisotropic Kitaev system is also discussed. △ Less

Submitted 14 November, 2018; originally announced November 2018.

Comments: 8 pages, 7 figures

Journal ref: Phys. Rev. B 99, 104408 (2019)