Showing 1–50 of 120 results for author: Capponi, S

Phase transitions in coupled Ising chains and SO($N$)-symmetric spin chains

Authors: Yohei Fuji, Sylvain Capponi, Lukas Devos, Philippe Lecheminant

Abstract: We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of $N$ copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of $N$ order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladde… ▽ More We investigate the nature of quantum phase transitions in a (1+1)-dimensional field theory composed of $N$ copies of the Ising conformal field theory interacting via competing relevant perturbations. The field theory governs the competition between a mass term and an interaction involving the product of $N$ order-parameter fields, which is realized, e.g. in coupled Ising chains, two-leg spin ladders, and SO($N$)-symmetric spin chains. By combining a perturbative renormalization group analysis and large-scale matrix-product state simulations, we systematically determine the nature of the phase transition as a function of $N$. For $N=2$ and $N=3$, we confirm that the transition is continuous, belonging to the Ising and four-state Potts universality classes, respectively. In contrast, for $N \ge 4$, our results provide compelling evidence that the transition becomes first order. We further apply these findings to specific lattice models with SO($N$) symmetry, including spin-$1/2$ and spin-$1$ two-leg ladders, that realize a direct transition between an SO($N$) symmetry-protected topological phase and a trivial phase. Our results refine a recent conjecture regarding the criticality of transitions between SPT phases. △ Less

Submitted 14 July, 2026; v1 submitted 18 February, 2026; originally announced February 2026.

Comments: 24 pages, 15 figures, v3: Updated upon journal acceptance

Variational study of the magnetization plateaus in the spin-1/2 kagome Heisenberg antiferromagnet: an approach from vision transformer neural quantum states

Authors: Andreas Raikos, Sylvain Capponi, Fabien Alet

Abstract: We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wavefunctions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$, $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regar… ▽ More We analyze the magnetization curve of the spin-1/2 kagome Heisenberg model in a magnetic field. Using state-of-the-art variational wavefunctions based on neural networks, we confirm the presence of robust magnetization plateaus at $m=1/3$, $5/9$ and $7/9$ of the saturation value, stabilized by a spontaneous symmetry breaking of lattice translations with a $\sqrt{3}\times \sqrt{3}$ unit cell. Regarding the more challenging $m=1/9$ plateau, we find two competing valence bond crystals depending on the system size, both breaking translation as well as point group symmetries and with a larger $3\times 3$ unit cell. Such quantum states with local modulations of the magnetization average values could be observed experimentally in the near future. △ Less

Submitted 13 February, 2026; originally announced February 2026.

Comments: 16 pages, 9 figures

Magnetic field-induced phases in a model S=1 Haldane chain system

Authors: I. Jakovac, M. S. Grbić, M. Dupont, N. Laflorencie, S. Capponi, Y. Hosokoshi, S. Krämer, Y. Skourski, S. Luther M. Takigawa, M. Horvatić

Abstract: An $S=1$ Haldane chain is a one-dimensional (1D) quantum magnet where strong fluctuations result in quantum disordered singlet ground state with a gapped excitation spectrum. The gap magnitude is primarily set by the dominant intrachain interaction ($J_\text{1D}$). An applied magnetic field closes the gap at $B_\text{c1}$ and drives the system into a gapless Tomonaga-Luttinger liquid (TLL) regime,… ▽ More An $S=1$ Haldane chain is a one-dimensional (1D) quantum magnet where strong fluctuations result in quantum disordered singlet ground state with a gapped excitation spectrum. The gap magnitude is primarily set by the dominant intrachain interaction ($J_\text{1D}$). An applied magnetic field closes the gap at $B_\text{c1}$ and drives the system into a gapless Tomonaga-Luttinger liquid (TLL) regime, followed by, at lower temperatures, a Bose-Einstein condensate (BEC) ground state, persisting up to $B_\text{c2} \propto 4 J_\text{1D}/gμ_B$. Almost all previously studied experimental realizations of such systems were based on transition-metal complexes which typically suffer from intrinsic anisotropies or large $J_\text{1D}$ values, limiting the access to the full theoretical phase diagram. We report a comprehensive study of TLL and BEC phases in the organic Haldane chain system 3,5-bis(N-tert-butylaminoxyl)-3'-nitrobiphenyl (BoNO). The absence of anisotropy and a moderate $J_\text{1D}$ enable exploration of the complete $B-T$ phase diagram. Through $^1$H nuclear magnetic resonance, combined with theoretical analysis, we characterize the TLL properties, map the BEC phase boundary $T_c (B)$, determine the associated critical exponent $ν\approx 0.66$ at $B_\text{c2}$, and demonstrate universal quasiparticle scaling in the quantum-critical regime. These results provide full experimental validation of theoretical predictions for field-induced phases in an $S=1$ Haldane chain, made over two decades ago. △ Less

Submitted 15 January, 2026; originally announced January 2026.

Comments: 8 pages, 3 figures

Understanding Structural Representation in Foundation Models for Polymers

Authors: Nathaniel H. Park, Eduardo Soares, Victor Y. Shirasuna, Tiffany J. Callahan, Sara Capponi, Emilio Vital Brazil

Abstract: From the relative scarcity of training data to the lack of standardized benchmarks, the development of foundation models for polymers face significant and multi-faceted challenges. At the core, many of these issues are tied directly to the structural representation of polymers and here, we present a new foundation model using a SMILES-based polymer graph representation. This approach allows repres… ▽ More From the relative scarcity of training data to the lack of standardized benchmarks, the development of foundation models for polymers face significant and multi-faceted challenges. At the core, many of these issues are tied directly to the structural representation of polymers and here, we present a new foundation model using a SMILES-based polymer graph representation. This approach allows representation of critical polymer architectural features and connectivity that are not available in other SMILES-based representations. The developed polymer foundation model exhibited excellent performance on 28 different benchmark datasets. Critical evaluation of the developed representation against other variations in control experiments reveals this approach to be a highly performant method of representing polymers in language-based foundation models. These control experiments also reveal a strong invariance of all SMILES representations, with many variations achieving state-of-the-art or near state-of-the-art performance, including those which are chemically or semantically invalid. Examination of error sources and attention maps for the evaluated representations corroborate the findings of the control experiments, showing that chemistry language models based on SMILES interpolate over all sequence space for prediction tasks, not only those of semantically valid inputs. Overall, this work highlights the importance of control experiments as a check on human-imposed assumptions that can limit rational design of both chemistry foundation models and their underlying structural representations. △ Less

Submitted 8 December, 2025; originally announced December 2025.

Critical Berezinskii-Kosterlitz-Thouless dynamics in the archetypal two-dimensional spin system Ba$_2$CuSi$_2$O$_6$Cl$_2$

Authors: K. M. Ranjith, Maxime Dupont, Steffen Krämer, Sylvain Capponi, Edmond Orignac, Nicolas Laflorencie, Nobuyuki Kurita, Hidekazu Tanaka, Mladen Horvatić

Abstract: We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature p… ▽ More We study the spin dynamics in the quasi-2D spin-$1/2$ dimer compound Ba$_2$CuSi$_2$O$_6$Cl$_2$, which exhibits a magnetic field-induced Bose-Einstein condensate (BEC) of triplons. Using nuclear magnetic resonance spin-lattice relaxation rate ($T_1^{-1}$) measurements combined with large-scale quantum Monte Carlo (QMC) simulations, we investigate critical fluctuations across the field-temperature phase diagram. Bridging the behavior observed in 1D and 3D systems, the $T_1^{-1}$ relaxation rate shows a pronounced peak extending well above the Néel temperature $T_N$, indicating strong two-dimensional Berezinskii-Kosterlitz-Thouless (BKT)-type fluctuations. A quantitative match between experimental and theoretical BEC phase boundaries validates an effective XXZ model. The study determines the intrinsic BKT transition temperature $T_{\mathrm{BKT}}$ from QMC, revealing a nearly field-independent $T_{\mathrm{BKT}}/T_N \approx 0.74$. Scaling analysis of the relaxation rate shows critical exponents consistent with 2D universality, and a narrow temperature window is identified where 2D physics dominates. These findings establish Ba$_2$CuSi$_2$O$_6$Cl$_2$ as a model system for exploring BKT dynamics in quantum magnets. △ Less

Submitted 10 June, 2026; v1 submitted 21 November, 2025; originally announced November 2025.

Comments: 12 pages, 11 figures

Journal ref: Phys. Rev. B 113 (2026) 224409

Detecting the Largest Correlations using the Correlation Density Matrix: a Quantum Monte Carlo Approach

Authors: Aditya Chincholi, Sylvain Capponi, Fabien Alet

Abstract: We present a quantum Monte Carlo-based approach to detect and compute the most dominant correlations for many-body systems without prior knowledge. It is based on the measurement and analysis of the correlation density matrix between two (small) subsystems embedded in the full (large) sample. In order to benchmark this procedure, we investigate zero-temperature quantum phase transitions in one- an… ▽ More We present a quantum Monte Carlo-based approach to detect and compute the most dominant correlations for many-body systems without prior knowledge. It is based on the measurement and analysis of the correlation density matrix between two (small) subsystems embedded in the full (large) sample. In order to benchmark this procedure, we investigate zero-temperature quantum phase transitions in one- and two-dimensional quantum Ising model as well as the two-dimensional bilayer Heisenberg antiferromagnet. The method paves the way for a systematic identification of unknown or exotic order parameters in unexplored phases on large systems accessible to quantum Monte Carlo methods. △ Less

Submitted 19 November, 2025; v1 submitted 29 July, 2025; originally announced July 2025.

Comments: 15 pages, 14 figures, 7 tables

Journal ref: Phys. Rev. B 113, 035122 (2026)

Coupling quantum spin ice to matter on the centered pyrochlore lattice

Authors: Rajah P. Nutakki, Sylvain Capponi, Ludovic D. C. Jaubert, Lode Pollet

Abstract: The low-energy physics of quantum spin ice is known to support an emergent form of quantum electrodynamics (QED), where magnetic monopoles exist and the fine structure constant is material dependent. In this article, we show how this QED is modified via a coupling to dynamical matter on the centered pyrochlore lattice, a structure which has recently been synthesized using metal-organic frameworks.… ▽ More The low-energy physics of quantum spin ice is known to support an emergent form of quantum electrodynamics (QED), where magnetic monopoles exist and the fine structure constant is material dependent. In this article, we show how this QED is modified via a coupling to dynamical matter on the centered pyrochlore lattice, a structure which has recently been synthesized using metal-organic frameworks. Specifically, we study the low-energy properties of the $S = 1/2$ quantum XXZ model on the centered pyrochlore lattice, with a focus on the sign-problem free region. At fourth order in degenerate perturbation theory this model hosts a quantum spin liquid distinct from the well-known U(1) quantum spin ice on the pyrochlore due to the presence of dynamical matter in the ground state. Exact diagonalization results are consistent with this quantum spin liquid over an extended region of the ground state phase diagram although potential quantum critical points within this region could indicate a richer phase structure. Our work thus expands the physics of quantum spin ice in an experimentally motivated geometry, showing how the emergent QED can be coupled to dynamical matter at zero temperature. △ Less

Submitted 24 October, 2025; v1 submitted 21 May, 2025; originally announced May 2025.

Comments: 23 pages, 20 figures, updated published version

Journal ref: Phys. Rev. B 112, 144437 (2025)

Simulating Bulk Gap in Chiral Projected Entangled-Pair States

Authors: Ji-Yao Chen, Yi Tan, Sylvain Capponi, Didier Poilblanc, Fei Ye, Jia-Wei Mei

Abstract: Projected entangled-pair states (PEPS) have proven effective in capturing chiral spin liquid ground states, yet the presence of long-range ``gossamer'' correlation tails raises concerns about their ability to accurately describe bulk gaps. Here, we address this challenge and demonstrate that PEPS can reliably characterize gapped bulk excitations in chiral topological phases. Using a variational pr… ▽ More Projected entangled-pair states (PEPS) have proven effective in capturing chiral spin liquid ground states, yet the presence of long-range ``gossamer'' correlation tails raises concerns about their ability to accurately describe bulk gaps. Here, we address this challenge and demonstrate that PEPS can reliably characterize gapped bulk excitations in chiral topological phases. Using a variational principle for excited states within a local mode approximation, we establish that correlation functions decaying faster than $r^{-2}$ are not necessarily related to gapless modes and thus long-range ``gossamer'' correlation tails in chiral PEPS do not contradict the presence of a bulk gap. This framework is validated in the spin-$\frac{1}{2}$ Kitaev model with a chiral term, where PEPS yields excitation gaps that agree well with exact solutions. Extending our approach to the $\mathbb{Z}_3$ Kitaev model, we present compelling evidence for its chiral ground state and accurately resolve its gapped excitations. These findings thus solidify PEPS as a powerful tool for studying both ground and excited states in chiral topological systems, thereby bridging a key gap in the understanding of their bulk properties. △ Less

Submitted 27 February, 2025; originally announced February 2025.

Comments: 4 figures in 6 pages

Classical and quantum spin liquids

Authors: Sylvain Capponi

Abstract: When considering magnetic systems in the thermodynamic limit and at low enough temperature, one finds typically magnetically ordered phases. In contrast, in the high-temperature regime, the interactions between the spin degrees of freedom become less relevant and the system loses its order: this is a paramagnet. This phenomenon of phase transition has been well understood using statistical mechani… ▽ More When considering magnetic systems in the thermodynamic limit and at low enough temperature, one finds typically magnetically ordered phases. In contrast, in the high-temperature regime, the interactions between the spin degrees of freedom become less relevant and the system loses its order: this is a paramagnet. This phenomenon of phase transition has been well understood using statistical mechanics and simple modelling. In these short lecture notes, we will review the possibility that a many-body magnetic system may remain magnetically disordered down to zero-temperature, both for classical or quantum spins. These exotic phases of matter are known, respectively, as classical and quantum spin liquids. We will address in particular the question of classification of these classical or quantum disordered phases. Indeed, while they have no local order parameter by definition, they can still possess different qualitative features related e.g. to the nature of their correlations or elementary excitations, which could be probed experimentally. △ Less

Submitted 24 January, 2025; originally announced January 2025.

Comments: lecture notes from a talk given at the IHP workshop about "Open questions in the quantum many-body problem" organized by Yvan Castin and Carlos Sá de Melo

Journal ref: Comptes Rendus. Physique, Volume 26 (2025), pp. 91-111

Evidence for a $\mathbb{Z}_{2}$ Dirac spin liquid in the generalized Shastry-Sutherland model

Authors: Atanu Maity, Francesco Ferrari, Sylvain Capponi, Karlo Penc, Janik Potten, Tobias Müller, Andreas Feuerpfeil, Ronny Thomale, Jong Yeon Lee, Rhine Samajdar, Yasir Iqbal

Abstract: We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-$1/2$ Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ansätze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_2$ states. Using density-matrix renormalization group (DMRG) and exac… ▽ More We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-$1/2$ Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ansätze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_2$ states. Using density-matrix renormalization group (DMRG) and exact diagonalization calculations, we find that the Shastry-Sutherland model and the square-lattice $J_1$-$J_2$ Heisenberg antiferromagnet share the same QSL phase. Motivated by this observation, we establish an explicit mapping of our Ansätze to those on the square lattice, and identify the counterpart of the square-lattice $\mathbb{Z}_2$ Dirac QSL (Z2A$zz$13) in the Shastry-Sutherland system. Employing state-of-the-art variational Monte Carlo calculations with Gutzwiller-projected wavefunctions, further improved by Lánczos steps, we demonstrate excellent agreement in both energies and correlation functions between a gapless (Dirac) $\mathbb{Z}_2$ spin liquid-characterized by only a few variational parameters-and results obtained from neural quantum states and DMRG. Finally, we apply the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group to compute the dynamical spin structure factor. The resulting spectra exhibit features consistent with Dirac cones in the excitation spectrum, providing strong independent evidence for a Dirac QSL ground state. Our identification of a $d$-wave pairing $\mathbb{Z}_2$ Dirac QSL is consistent with recently observed signatures of QSL behavior in Pr$_2$Ga$_2$BeO$_7$ and outlines predictions for future experiments. △ Less

Submitted 16 March, 2026; v1 submitted 30 December, 2024; originally announced January 2025.

Comments: 52 pages, 36 figures, 16 tables

Phase transitions and remnants of fractionalization at finite temperature in the triangular lattice quantum loop model

Authors: Xiaoxue Ran, Sylvain Capponi, Junchen Rong, Fabien Alet, Zi Yang Meng

Abstract: The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg arrays quantum simulators. However, how the thermal fluctuations interact wi… ▽ More The quantum loop and dimer models are archetypal correlated systems with local constraints. With natural foundations in statistical mechanics, they are of direct relevance to various important physical concepts and systems, such as topological order, lattice gauge theories, geometric frustrations, or more recently Rydberg arrays quantum simulators. However, how the thermal fluctuations interact with constraints has not been explored in the important class of non-bipartite geometries. Here we study, via unbiased quantum Monte Carlo simulations and field theoretical analysis, the finite-temperature phase diagram of the quantum loop model on the triangular lattice. We discover that the recently identified, "hidden" vison plaquette (VP) quantum crystal [1] experiences a finite-temperature continuous transition, which smoothly connects to the (2+1)d Cubic* quantum critical point separating the VP and $\mathbb{Z}_{2}$ quantum spin liquid phases. This finite-temperature phase transition acquires a unique property of ``remnants of fractionalization" at finite temperature, in that, both the cubic order parameter -- the plaquette loop resonance -- and its constituent -- the vison field -- exhibit independent criticality signatures. This phase transition is connected to a 3-state Potts transition between the lattice nematic phase and the high-temperature disordered phase. We discuss the relevance of our results for current experiments on quantum simulation platforms. △ Less

Submitted 25 November, 2025; v1 submitted 2 December, 2024; originally announced December 2024.

Comments: 8+10 pages, 4+7 figures

Journal ref: Physical Review Letter, Vol. 135, Iss. 12, 12 September 2025

Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains

Authors: Sylvain Capponi, Lukas Devos, Philippe Lecheminant, Keisuke Totsuka, Laurens Vanderstraeten

Abstract: We investigate the nature of the quantum phase transition in modulated SU(N) Heisenberg spin chains. In the odd-N case, the transition separates a trivial non-degenerate phase to a doubly-degenerate gapped chiral PSU(N) symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the… ▽ More We investigate the nature of the quantum phase transition in modulated SU(N) Heisenberg spin chains. In the odd-N case, the transition separates a trivial non-degenerate phase to a doubly-degenerate gapped chiral PSU(N) symmetry-protected topological (SPT) phase which breaks spontaneously the inversion symmetry. The transition is not an Ising transition associated to the breaking of the $\mathbb{Z}_2$ inversion symmetry, but is governed by the delocalization of the edge states of the SPT phase. In this respect, a modulated SU(N) Heisenberg spin chain provides a simple example in one dimension of a non-Landau phase transition which is described by the SU(N)$_1$ conformal field theory. We show that the chiral SPT phase exhibits fractionalized spinon excitations, which can be confined by changing the model parameters slightly. △ Less

Submitted 2 September, 2024; originally announced September 2024.

Comments: 13 pages, 12 figures

Journal ref: Phys. Rev. B 111, L020404 (2025)

Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models

Authors: Attila Szabó, Sylvain Capponi, Fabien Alet

Abstract: Using high-accuracy variational Monte Carlo based on group-convolutional neural networks (GCNNs), we obtain the symmetry-resolved low-energy spectrum of the spin-1/2 Heisenberg model on several highly symmetric fullerene geometries, including the famous C$_{60}$ buckminsterfullerene. We argue that as the degree of frustration is lowered in large fullerenes, they display characteristic features of… ▽ More Using high-accuracy variational Monte Carlo based on group-convolutional neural networks (GCNNs), we obtain the symmetry-resolved low-energy spectrum of the spin-1/2 Heisenberg model on several highly symmetric fullerene geometries, including the famous C$_{60}$ buckminsterfullerene. We argue that as the degree of frustration is lowered in large fullerenes, they display characteristic features of incipient magnetic ordering: correlation functions show high-intensity Bragg peaks consistent with Néel-like ordering, while the low-energy spectrum is organised into a tower of states. Competition with frustration, however, turns the simple Néel order into a noncoplanar one. Remarkably, we find and predict chiral incipient ordering in a large number of fullerene structures. △ Less

Submitted 9 February, 2024; v1 submitted 2 November, 2023; originally announced November 2023.

Comments: 14+3 pages, 14 figures, 3+4 tables. v2: close to published version

Journal ref: Phys. Rev. B 109, 054410 (2024)

Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice

Authors: Yi Xu, Sylvain Capponi, Ji-Yao Chen, Laurens Vanderstraeten, Juraj Hasik, Andriy H. Nevidomskyy, Matthieu Mambrini, Karlo Penc, Didier Poilblanc

Abstract: Motivated by the search for chiral spin liquids (CSL), we consider a simple model defined on the kagome lattice of interacting SU(3) spins (in the fundamental representation) including two-site and three-site permutations between nearest neighbor sites and on triangles, respectively. By combining analytical developments and various numerical techniques, namely exact Lanczos diagonalizations and te… ▽ More Motivated by the search for chiral spin liquids (CSL), we consider a simple model defined on the kagome lattice of interacting SU(3) spins (in the fundamental representation) including two-site and three-site permutations between nearest neighbor sites and on triangles, respectively. By combining analytical developments and various numerical techniques, namely exact Lanczos diagonalizations and tensor network variational approaches, we find a rich phase diagram with non-topological (``trivial") and topological (possibly chiral) gapped spin liquids (SLs). Trivial spin liquids include an Affleck-Kennedy-Lieb-Tasaki (AKLT)-like phase and a trimerized phase, the latter breaking the inversion center between the up and down triangles of the kagome lattice. A topological SL is stabilized in a restricted part of the phase diagram by the time-reversal symmetry breaking (complex) 3-site permutation term. Analyzing the chiral edge modes of this topological SL on long cylinders or on finite disks, we have come up with two competing scenarios, either a CSL or a double Chern-Simon SL characterized by a single or by two counter-propagating Wess-Zumino-Witten SU(3)$_1$ chiral mode(s), respectively. In the vicinity of the extended ferromagnetic region we have found a magnetic phase corresponding either to a modulated canted ferromagnet or to a uniform partially magnetized ferromagnet. △ Less

Submitted 28 June, 2023; originally announced June 2023.

Comments: 24 pages, 25 figures, 4 tables

Journal ref: Phys. Rev. B 108, 195153 (2023)

Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet

Authors: Alexander Wietek, Sylvain Capponi, Andreas M. Läuchli

Abstract: Quantum electrodynamics in $2+1$ dimensions (QED$_3$) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated $J_1$-$J_2$ Heisenberg model… ▽ More Quantum electrodynamics in $2+1$ dimensions (QED$_3$) has been proposed as a critical field theory describing the low-energy effective theory of a putative algebraic Dirac spin liquid or of quantum phase transitions in two-dimensional frustrated magnets. We provide compelling evidence that the intricate spectrum of excitations of the elementary but strongly frustrated $J_1$-$J_2$ Heisenberg model on the triangular lattice is in one-to-one correspondence to a zoo of excitations from QED$_3$, in the quantum spin liquid regime. This includes a large manifold of explicitly constructed monopole and bilinear excitations of QED$_3$, which is thus shown to serve as an organizing principle of phases of matter in triangular lattice antiferromagnets and their low-lying excitations. Moreover, we observe signatures of an emergent valence bond solid (VBS), which suggests a scenario where only the critical point of a transition from the $120^\circ$ Néel order to a VBS is described by QED$_3$. Our results are obtained by comparing ansatz wave functions from a parton construction to exact eigenstates obtained using large-scale exact diagonalization up to $N=48$ sites. △ Less

Submitted 3 July, 2024; v1 submitted 2 March, 2023; originally announced March 2023.

Comments: 8 pages, 5 figures, including supplementary material

Journal ref: Phys. Rev. X 14, 021010 (2024)

Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

Authors: Loïc Herviou, Sylvain Capponi, Philippe Lecheminant

Abstract: The zero-temperature phase diagram of the $J_1-J_2$ SU($N$) antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped SU($N$) valence bond solid made of $N$ sites is formed above a critical value of $J_2/J_1$ for all $N$. We find that the extension of this $N$-merized phase for larger values of $J_2$ stro… ▽ More The zero-temperature phase diagram of the $J_1-J_2$ SU($N$) antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped SU($N$) valence bond solid made of $N$ sites is formed above a critical value of $J_2/J_1$ for all $N$. We find that the extension of this $N$-merized phase for larger values of $J_2$ strongly depends on the parity of $N$. For even $N$, the phase smoothly interpolates to the large $J_2$ regime where the model can be viewed as a zigzag SU($N$) two-leg spin ladder. The phase exhibits both a $N$-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the $N$-merized phase with odd $N$ only has a finite extent with no incommensuration. A gapless phase in the SU($N$)$_1$ universality class is stabilized for larger $J_2$ that stems from the existence of a massless renormalization group flow from SU($N$)$_2$ to SU($N$)$_1$ conformal field theories when $N$ is odd. △ Less

Submitted 22 May, 2023; v1 submitted 27 February, 2023; originally announced February 2023.

Comments: Final version

Journal ref: Phys. Rev. B 107, 205135 (2023)

Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders

Authors: Juraj Hasik, Glen B. Mbeng, Sylvain Capponi, Federico Becca, Andreas M. Läuchli

Abstract: Infinite projected entangled-pair states (iPEPS) have been introduced to accurately describe many-body wave functions on two-dimensional lattices. In this context, two aspects are crucial: the systematic improvement of the {\it Ansatz} by the optimization of its building blocks, i.e., tensors characterized by bond dimension $D$, and the extrapolation scheme to reach the "thermodynamic" limit… ▽ More Infinite projected entangled-pair states (iPEPS) have been introduced to accurately describe many-body wave functions on two-dimensional lattices. In this context, two aspects are crucial: the systematic improvement of the {\it Ansatz} by the optimization of its building blocks, i.e., tensors characterized by bond dimension $D$, and the extrapolation scheme to reach the "thermodynamic" limit $D \to \infty$. Recent advances in variational optimization and scaling based on correlation lengths demonstrated the ability of iPEPS to capture the spontaneous breaking of a continuous symmetry in phases such as the antiferromagnetic (Néel) phase with high fidelity, in addition to valence-bond solids which are already well described by finite-$D$ iPEPS. In contrast, systems in the vicinity of continuous quantum phase transitions still present a challenge for iPEPS, especially when non-abelian symmetries are involved. Here, we consider the iPEPS Ansatz to describe the continuous transition between the (gapless) antiferromagnet and the (gapped) paramagnet that exists in the $S=1/2$ Heisenberg model on coupled two-leg ladders. In particular, we show how accurate iPEPS results can be obtained down to a narrow interval around criticality and analyze the scaling of the order parameter in the Néel phase in a spatially anisotropic situation. △ Less

Submitted 13 June, 2022; originally announced June 2022.

Comments: 9 pages, 7 figures, source code available at https://github.com/jurajHasik/peps-torch

Journal ref: Phys. Rev. B 106, 125154 (2022)

Weakly first-order quantum phase transition between Spin Nematic and Valence Bond Crystal Order in a square lattice SU(4) fermionic model

Authors: Pranay Patil, Fabien Alet, Sylvain Capponi, Matthieu Mambrini

Abstract: We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultracold atom experiments and existence of spin liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simu… ▽ More We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultracold atom experiments and existence of spin liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simulations without a sign problem. We find evidence for spin nematic and valence bond crystalline phases, which are separated by a weak first order phase transition. A U(1) symmetry is found to emerge in the valence bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained with the help of a loop algorithm which allows large-scale simulations of bilinear-biquadratic SO(N ) models on arbitrary lattices in a certain parameter regime. △ Less

Submitted 4 May, 2022; v1 submitted 21 September, 2021; originally announced September 2021.

Comments: 6+7 pages, 8 figures

Journal ref: Phys. Rev. B 105, L140403 (2022)

Abelian SU$(N)_1$ Chiral Spin Liquids on the Square Lattice

Authors: Ji-Yao Chen, Jheng-Wei Li, Pierre Nataf, Sylvain Capponi, Matthieu Mambrini, Keisuke Totsuka, Hong-Hao Tu, Andreas Weichselbaum, Jan von Delft, Didier Poilblanc

Abstract: In the physics of the Fractional Quantum Hall (FQH) effect, a zoo of Abelian topological phases can be obtained by varying the magnetic field. Aiming to reach the same phenomenology in spin-like systems, we propose a family of SU($N$)-symmetric models in the fundamental representation, on the square lattice with short-range interactions restricted to triangular units, a natural generalization for… ▽ More In the physics of the Fractional Quantum Hall (FQH) effect, a zoo of Abelian topological phases can be obtained by varying the magnetic field. Aiming to reach the same phenomenology in spin-like systems, we propose a family of SU($N$)-symmetric models in the fundamental representation, on the square lattice with short-range interactions restricted to triangular units, a natural generalization for arbitrary $N$ of an SU($3$) model studied previously where time-reversal symmetry is broken explicitly. Guided by the recent discovery of SU($2$)$_1$ and SU($3$)$_1$ chiral spin liquids (CSL) on similar models we search for topological SU($N$)$_1$ CSL in some range of the Hamiltonian parameters via a combination of complementary numerical methods such as exact diagonalizations (ED), infinite density matrix renormalization group (iDMRG) and infinite Projected Entangled Pair State (iPEPS). Extensive ED on small (periodic and open) clusters up to $N=10$ and an innovative SU($N$)-symmetric version of iDMRG to compute entanglement spectra on (infinitely-long) cylinders in all topological sectors provide unambiguous signatures of the SU($N$)$_1$ character of the chiral liquids. An SU($4$)-symmetric chiral PEPS, constructed in a manner similar to its SU($2$) and SU($3$) analogs, is shown to give a good variational ansatz of the $N=4$ ground state, with chiral edge modes originating from the PEPS holographic bulk-edge correspondence. Finally, we discuss the possible observation of such Abelian CSL in ultracold atom setups where the possibility of varying $N$ provides a tuning parameter similar to the magnetic field in the physics of the FQH effect. △ Less

Submitted 8 October, 2021; v1 submitted 3 June, 2021; originally announced June 2021.

Comments: 41 pages, 21 figures, references added, figure 2(j) modified, abstract and introduction revised

Quantum half-orphans in kagome antiferromagnets

Authors: Pranay Patil, Fabien Alet, Sylvain Capponi, Kedar Damle

Abstract: We numerically study the effects of non-magnetic impurities (vacancies) in the spin-$S$ Heisenberg antiferromagnet on the kagomé lattice. For a range of low but nonzero temperatures, and spin values that extend down to $S=2$, we find that the magnetization response to an external magnetic field is consistent with the response of emergent "half-orphan" degrees of freedom that are expected to domina… ▽ More We numerically study the effects of non-magnetic impurities (vacancies) in the spin-$S$ Heisenberg antiferromagnet on the kagomé lattice. For a range of low but nonzero temperatures, and spin values that extend down to $S=2$, we find that the magnetization response to an external magnetic field is consistent with the response of emergent "half-orphan" degrees of freedom that are expected to dominate the response of the corresponding classical magnet in a similar temperature range whenever there are two vacancies on the same triangle. Specifically, for all spin values we have considered (from $S=1/2$ to $S=4$), there is a large enhancement of the local susceptibility of the lone spin on such a triangle with two vacancies; in the presence of a uniform magnetic field $h$, this lone-spin behaves effectively as an almost free spin $S$ in an effective field $h/2$. Quite remarkably, in the zero temperature limit, the ground state in the presence of a half-orphan has a non-zero total spin value $S_{GS}$ that shows a trend similar to $S/2$ when $S\ge 2$. These qualitative aspects of the response differ strikingly from the more conventional response of diluted samples without such half-orphan degrees of freedom. We discuss how these findings could be checked experimentally. △ Less

Submitted 4 January, 2021; v1 submitted 3 September, 2020; originally announced September 2020.

Comments: 15 pages, 15 figures

Journal ref: Phys. Rev. Research 2, 043425 (2020)

Quantum spin liquid phases in the bilinear-biquadratic two-SU(4)-fermion Hamiltonian on the square lattice

Authors: Olivier Gauthé, Sylvain Capponi, Matthieu Mambrini, Didier Poilblanc

Abstract: We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (ie self-conjugate $\bf 6$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimer-like phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauthé, S. Capponi and… ▽ More We consider the phase diagram of the most general SU(4)-symmetric two-site Hamiltonian for a system of two fermions per site (ie self-conjugate $\bf 6$ representation) on the square lattice. It is known that this model hosts magnetic phases breaking SU(4) symmetry and quantum disordered dimer-like phases breaking lattice translation symmetry. Motivated by a previous work [O. Gauthé, S. Capponi and D. Poilblanc, Phys. Rev. B $\textbf{99}$, 241112(R) (2019)], we investigate the possibility of the existence of SU(4) quantum spin liquid phases in this model, using SU(4)-symmetric Projected Entangled Pair States (PEPS) of small bond dimensions, which can be classified according to point group and charge (C) symmetries. Among several (disconnected) families of SU(4)-symmetric PEPS, breaking or not C-symmetry, we identify critical or topological spin liquids which may be stable in some regions of the phase diagram. These results are confronted to exact diagonalisation (ED) and density matrix renormalisation group (DMRG) calculations. △ Less

Submitted 25 October, 2020; v1 submitted 13 February, 2020; originally announced February 2020.

Journal ref: Phys. Rev. B 101, 205144 (2020)

SU$(3)_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS

Authors: Ji-Yao Chen, Sylvain Capponi, Alexander Wietek, Matthieu Mambrini, Norbert Schuch, Didier Poilblanc

Abstract: Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU$(3)_1$ chiral spin liquid on the square lattice. Characteristic features are revealed by the entanglement sp… ▽ More Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS). Guided by extensive exact diagonalization and density matrix renormalization group calculations, we construct an optimized symmetric PEPS for a SU$(3)_1$ chiral spin liquid on the square lattice. Characteristic features are revealed by the entanglement spectrum (ES) on an infinitely long cylinder. In all three $\mathbb{Z}_3$ sectors, the level counting of the linear dispersing modes is in full agreement with SU$(3)_1$ Wess-Zumino-Witten conformal field theory prediction. Special features in the ES are shown to be in correspondence with bulk anyonic correlations, indicating a fine structure in the holographic bulk-edge correspondence. Possible universal properties of topological SU$(N)_k$ chiral PEPS are discussed. △ Less

Submitted 23 January, 2020; v1 submitted 31 December, 2019; originally announced December 2019.

Comments: v1: 6+23 pages, 4+13 figures, 0+27 tables. v2: add one figure in supplemental material, add one reference

Journal ref: Phys. Rev. Lett. 125, 017201 (2020)

Ground-state properties of the one-dimensional Hubbard model with pairing potential

Authors: Myung-Hoon Chung, Edmond Orignac, Didier Poilblanc, Sylvain Capponi

Abstract: We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. Guided by analytic bosonization results, we quantitatively determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By… ▽ More We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. Guided by analytic bosonization results, we quantitatively determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By computing various local quantities as well as the half-system entanglement, we are able to distinguish between Mott, metallic and superconducting phases. We point out the compressible nature of the Mott phase and the fully gapped nature of the many-body spectrum of the superconducting phase, in the presence of explicit U(1)-charge symmetry breaking. △ Less

Submitted 26 September, 2020; v1 submitted 21 December, 2019; originally announced December 2019.

Comments: 26 pages, 8 figures

Journal ref: Physica B: Condensed Matter, Volume 604, 412665 (2021)

Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins

Authors: Sylvain Capponi, Pierre Fromholz, Philippe Lecheminant, Keisuke Totsuka

Abstract: Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup $\mathbb{Z}_N \times \mathbb{Z}_N$) with $N>2$. The unique feature of these symmetry protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transfor… ▽ More Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup $\mathbb{Z}_N \times \mathbb{Z}_N$) with $N>2$. The unique feature of these symmetry protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transform, for instance, respectively in the fundamental ($\boldsymbol{N}$) and anti-fundamental ($\overline{\boldsymbol{N}}$) representations of SU($N$). We show, by means of complementary analytical and numerical approaches, that these chiral SPT phases as well as the non-chiral ones are realized as the ground states of a generalized two-leg SU($N$) spin ladder in which the spins in the first chain transform in $\boldsymbol{N}$ and the second in $\overline{\boldsymbol{N}}$. In particular, we map out the phase diagram for $N=3$ and $4$ to show that {\em all} the possible symmetry-protected topological phases with projective SU($N$)-symmetry appear in this simple ladder model. △ Less

Submitted 30 September, 2019; originally announced September 2019.

Comments: 21 pages

Journal ref: Phys. Rev. B 101, 195121 (2020)

Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

Authors: Didier Poilblanc, Matthieu Mambrini, Sylvain Capponi

Abstract: We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimer-dimer correlations -- typical of Rokhsar-Kivelson (RK) points of quantum dimer m… ▽ More We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimer-dimer correlations -- typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices -- while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point. △ Less

Submitted 11 September, 2019; v1 submitted 8 July, 2019; originally announced July 2019.

Comments: 19 pages, 8 figures, v2 minor modifications, 1 ref added

Journal ref: SciPost Phys. 7, 041 (2019)

NMR relaxation in the spin-1 Heisenberg chain

Authors: Sylvain Capponi, Maxime Dupont, Anders W. Sandvik, Pinaki Sengupta

Abstract: We consider the isotropic $S=1$ Heisenberg chain with a finite Haldane gap $Δ$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate $1/T_1$ measured in nuclear magnetic resonance (NMR) experiments for instance. In particular, we analyze the contributions from modes with momenta close to… ▽ More We consider the isotropic $S=1$ Heisenberg chain with a finite Haldane gap $Δ$ and use state-of-the-art numerical techniques to investigate its dynamical properties at finite temperature, focusing on the nuclear spin-lattice relaxation rate $1/T_1$ measured in nuclear magnetic resonance (NMR) experiments for instance. In particular, we analyze the contributions from modes with momenta close to $q\approx 0$ and $q\approx π$ as a function of temperature. At high-temperature, we observe spin diffusion with a non-trivial exponent. At low-temperature, we argue that a simple activated behavior $1/T_1 \propto\exp(-Δ/T)$ can only be observed at temperatures much smaller than the gap $Δ$. △ Less

Submitted 18 September, 2019; v1 submitted 29 May, 2019; originally announced May 2019.

Comments: published version

Journal ref: Phys. Rev. B 100, 094411 (2019)

SU(4) topological RVB spin liquid on the square lattice

Authors: Olivier Gauthé, Sylvain Capponi, Didier Poilblanc

Abstract: We generalize the construction of the spin-1/2 SU(2) Resonating Valence Bond (RVB) state to the case of the self-conjugate $\bf 6$-representation of SU(4). As for the case of SU(2) [J-Y. Chen and D. Poilblanc, Phys. Rev. B $\textbf{97}$, 161107(R) (2018)], we use the Projected Entangled Pair State (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the s… ▽ More We generalize the construction of the spin-1/2 SU(2) Resonating Valence Bond (RVB) state to the case of the self-conjugate $\bf 6$-representation of SU(4). As for the case of SU(2) [J-Y. Chen and D. Poilblanc, Phys. Rev. B $\textbf{97}$, 161107(R) (2018)], we use the Projected Entangled Pair State (PEPS) formalism to derive a simple (two-dimensional) family of generalized SU(4) RVB states on the square lattice. We show that, when longer-range SU(4)-singlet bonds are included, a local gauge symmetry is broken down from U(1) to $\mathbb{Z}_2$, leading to the emergence of a short-range spin liquid. Evidence for the topological nature of this spin liquid is provided by the investigation of the Renyi entanglement entropy of infinitely-long cylinders and of the modular matrices. Relevance to microscopic models and experiments of ultracold atoms is discussed. △ Less

Submitted 14 June, 2019; v1 submitted 17 January, 2019; originally announced January 2019.

Journal ref: Phys. Rev. B 99, 241112 (2019)

Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study

Authors: Ji-Yao Chen, Laurens Vanderstraeten, Sylvain Capponi, Didier Poilblanc

Abstract: Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the Fractional Quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by Exact Diagonalisation of small clusters. Using families of f… ▽ More Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the Fractional Quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by Exact Diagonalisation of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral Projected Entangled Pair States (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with Density Matrix Renormalisation Group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range "gossamer tails". We argue these tails are finite-$D$ artifacts of the chiral PEPS, which become irrelevant when the PEPS bond dimension $D$ is increased. From the investigation of the entanglement spectrum, we observe sharply defined chiral edge modes following the prediction of the SU(2)$_2$ Wess-Zumino-Witten theory and exhibiting a conformal field theory (CFT) central charge $c=3/2$, as expected for a Moore-Read chiral spin liquid. We conclude that the PEPS formalism offers an unbiased and efficient method to investigate non-Abelian chiral spin liquids in quantum antiferromagnets. △ Less

Submitted 14 July, 2018; v1 submitted 11 July, 2018; originally announced July 2018.

Comments: 15 pages, 16 figures - references added - small changes in title and abstract

Journal ref: Phys. Rev. B 98, 184409 (2018)

Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets

Authors: Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie, Edmond Orignac

Abstract: Theoretically challenging, the understanding of the dynamical response in quantum antiferromagnets is of great interest, in particular for both inelastic neutron scattering (INS) and nuclear magnetic resonance (NMR) experiments. In such a context, we theoretically address this question for quasi-one-dimensional quantum magnets, e.g. weakly coupled spin chains for which many compounds are available… ▽ More Theoretically challenging, the understanding of the dynamical response in quantum antiferromagnets is of great interest, in particular for both inelastic neutron scattering (INS) and nuclear magnetic resonance (NMR) experiments. In such a context, we theoretically address this question for quasi-one-dimensional quantum magnets, e.g. weakly coupled spin chains for which many compounds are available in Nature. In this class of systems, the dimensional crossover between a three-dimensional ordered regime at low temperature towards one-dimensional physics at higher temperature is a non-trivial issue, notably difficult concerning dynamical properties. Here we present a comprehensive theoretical study based on both analytical calculations (bosonization + random phase and self-consistent harmonic approximations) and numerical simulations (quantum Monte Carlo + stochastic analytic continuation) which allows us to describe the full temperature crossover for the NMR relaxation rate $1/T_1$, from one-dimensional Tomonaga-Luttinger liquid physics to the three-dimensional ordered regime, as a function of inter-chain couplings. The dynamical structure factor, directly probing the INS intensity, is also computed in the different regimes. △ Less

Submitted 6 September, 2018; v1 submitted 13 June, 2018; originally announced June 2018.

Comments: 18 pages, 7 figures

Journal ref: Phys. Rev. B 98, 094403 (2018)

Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model

Authors: Ji-Yao Chen, Sylvain Capponi, Didier Poilblanc

Abstract: Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice $π/2$-rotation symmetry. A supe… ▽ More Spontaneous discrete symmetry breaking can be described in the framework of Projected Entangled Pair States (PEPS) by linearly superposing local tensors belonging to two (or more) symmetry classes of tensors. This is illustrated in the case of a frustrated spin-1 Heisenberg model on the square lattice, which hosts a nematic spin liquid spontaneously breaking lattice $π/2$-rotation symmetry. A superposition of SU(2)-symmetric PEPS tensors belonging to two irreducible representations of the lattice point group is shown to capture accurately the properties of the nematic phase, as shown from a comparison to Exact Diagonalisations and Density Matrix Renormalization Group results. △ Less

Submitted 6 July, 2018; v1 submitted 30 March, 2018; originally announced March 2018.

Comments: 10 pages, 12 figures. V2: reference added. V3: reference added, published version

Journal ref: Phys. Rev. B 98, 045106 (2018)

Unified Phase Diagram of Antiferromagnetic SU(N) Spin Ladders

Authors: Andreas Weichselbaum, Sylvain Capponi, Philippe Lecheminant, Alexei M. Tsvelik, Andreas M. Läuchli

Abstract: Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg SU($N$) spin ladders. Two-leg ladders provide a rich and highly non-trivial extension of the single chain case on the way towards the relatively little explored two dimensional situation. Focusing on the experimentally relevant… ▽ More Motivated by near-term experiments with ultracold alkaline-earth atoms confined to optical lattices, we establish numerically and analytically the phase diagram of two-leg SU($N$) spin ladders. Two-leg ladders provide a rich and highly non-trivial extension of the single chain case on the way towards the relatively little explored two dimensional situation. Focusing on the experimentally relevant limit of one fermion per site, antiferromagnetic exchange interactions, and $2\leq N \leq 6$, we show that the phase diagrams as a function of the interchain (rung) to intrachain (leg) coupling ratio $J_\perp/J_\Vert$ strongly differ for even vs. odd $N$. For even $N=4$ and 6, we demonstrate that the phase diagram consists of a single valence bond crystal (VBC) with a spatial period of $N/2$ rungs. For odd $N=3$ and 5, we find surprisingly rich phase diagrams exhibiting three distinct phases. For weak rung coupling, we obtain a VBC with a spatial period of $N$ rungs, whereas for strong coupling we obtain a critical phase related to the case of a single chain. In addition, we encounter intermediate phases for odd $N$, albeit of a different nature for $N=3$ as compared to $N=5$. For $N=3$, we find a novel gapless intermediate phase with $J_\perp$-dependent incommensurate spatial fluctuations in a sizeable region of the phase diagram. For $N=5$, there are strong indications for a narrow potentially gapped intermediate phase, whose nature is not entirely clear. △ Less

Submitted 16 March, 2018; originally announced March 2018.

Comments: 12+10 pages

Journal ref: Phys. Rev. B 98, 085104 (2018)

Detection of a Disorder-Induced Bose-Einstein Condensate in a Quantum Spin Material at High Magnetic Fields

Authors: A. Orlova, H. Mayaffre, S. Krämer, M. Dupont, S. Capponi, N. Laflorencie, A. Paduan-Filho, M. Horvatić

Abstract: The coupled spin-1 chains material NiCl$_2$-4SC(NH$_2$)$_2$ (DTN) doped with Br impurities is expected to be a perfect candidate for observing many-body localization at high magnetic field: the so-called "Bose glass", a zero-temperature bosonic fluid, compressible, gapless, incoherent, and short-range correlated. Using nuclear magnetic resonance (NMR), we critically address the stability of the Bo… ▽ More The coupled spin-1 chains material NiCl$_2$-4SC(NH$_2$)$_2$ (DTN) doped with Br impurities is expected to be a perfect candidate for observing many-body localization at high magnetic field: the so-called "Bose glass", a zero-temperature bosonic fluid, compressible, gapless, incoherent, and short-range correlated. Using nuclear magnetic resonance (NMR), we critically address the stability of the Bose glass in doped DTN, and find that it hosts a novel disorder-induced ordered state of matter, where many-body physics leads to an unexpected resurgence of quantum coherence emerging from localized impurity states. An experimental phase diagram of this new "order-from-disorder" phase, established from NMR $T_1^{-1}$ relaxation rate data in the (13 $\pm$ 1)% Br-doped DTN, is found to be in excellent agreement with the theoretical prediction from large-scale quantum Monte Carlo simulations. △ Less

Submitted 29 October, 2018; v1 submitted 4 January, 2018; originally announced January 2018.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. Lett. 121, 177202 (2018)

Dynamical properties of the $S=\frac{1}{2}$ random Heisenberg chain

Authors: Yu-Rong Shu, Maxime Dupont, Dao-Xin Yao, Sylvain Capponi, Anders W. Sandvik

Abstract: We use numerical techniques to study dynamical properties at finite temperature ($T$) of the Heisenberg spin chain with random exchange couplings, which realizes the random singlet (RS) fixed point in the low-energy limit. Specifically, we study the dynamic spin structure factor $S(q,ω)$, which can be probed directly by inelastic neutron scattering experiments and, in the limit of small $ω$, in nu… ▽ More We use numerical techniques to study dynamical properties at finite temperature ($T$) of the Heisenberg spin chain with random exchange couplings, which realizes the random singlet (RS) fixed point in the low-energy limit. Specifically, we study the dynamic spin structure factor $S(q,ω)$, which can be probed directly by inelastic neutron scattering experiments and, in the limit of small $ω$, in nuclear magnetic resonance (NMR) experiments through the spin-lattice relaxation rate $1/T_1$. Our work combines three complementary methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Unlike the uniform system, whose low-energy excitations at low $T$ are restricted to $q$ close to $0$ and $π$, our study reveals a continuous narrow band of low-energy excitations in $S(q,ω)$, extending throughout the Brillouin zone. Close to $q=π$, the scaling properties of these excitations are well captured by the RS theory, but we also see disagreements with some aspects of the predicted $q$-dependence further away from $q=π$. Furthermore we find spin diffusion effects close to $q=0$ that are not contained within the RS theory but give non-negligible contributions to the mean $1/T_1$. To compare with NMR experiments, we consider the distribution of the local $1/T_1$ values, which is broad, approximately described by a stretched exponential. The mean value first decreases with $T$, but starts to increase and diverge below a crossover temperature. Although a similar divergent behavior has been found for the static uniform susceptibility, this divergent behavior of $1/T_1$ has never been seen in experiments. Our results show that the divergence of the mean $1/T_1$ is due to rare events in the disordered chains and is concealed in experiments, where the typical $1/T_1$ value is accessed. △ Less

Submitted 29 March, 2018; v1 submitted 5 December, 2017; originally announced December 2017.

Comments: 19 pages, 14 figures

Journal ref: Phys. Rev. B 97, 104424 (2018)

"Haldane" phases with ultracold fermionic atoms in double-well optical lattices

Authors: P. Fromholz, S. Capponi, P. Lecheminant, D. J. Papoular, K. Totsuka

Abstract: We propose to realize one-dimensional topological phases protected by SU($N$) symmetry using alkali or alkaline-earth atoms loaded into a bichromatic optical lattice. We derive a realistic model for this system and investigate it theoretically. Depending on the parity of $N$, two different classes of symmetry-protected topological (SPT) phases are stabilized at half-filling for physical parameters… ▽ More We propose to realize one-dimensional topological phases protected by SU($N$) symmetry using alkali or alkaline-earth atoms loaded into a bichromatic optical lattice. We derive a realistic model for this system and investigate it theoretically. Depending on the parity of $N$, two different classes of symmetry-protected topological (SPT) phases are stabilized at half-filling for physical parameters of the model. For even $N$, the celebrated spin-1 Haldane phase and its generalization to SU($N$) are obtained with no local symmetry breaking. In stark contrast, at least for $N=3$, a new class of SPT phases, dubbed chiral Haldane phases, that spontaneously break inversion symmetry, emerge with a two-fold ground-state degeneracy. The latter ground states with open-boundary conditions are characterized by different left and right boundary spins which are related by conjugation. Our results show that topological phases are within close reach of the latest experiments on cold fermions in optical lattices. △ Less

Submitted 29 September, 2017; originally announced September 2017.

Comments: 4 pages main article (4 figs.), 1 page acknowledgement and bibliography, 9 pages Supp. Mat. (8 figs.)

Journal ref: Phys. Rev. B 99, 054414 (2019)

Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet

Authors: Hui Shao, Yan Qi Qin, Sylvain Capponi, Stefano Chesi, Zi Yang Meng, Anders W. Sandvik

Abstract: We study the dynamic spin structure factor of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and of the $J$-$Q$ model (with 4-spin interactions $Q$ and Heisenberg exchange $J$). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp ($δ$-function) contribution from spinwaves (magnons) and… ▽ More We study the dynamic spin structure factor of the spin-$1/2$ square-lattice Heisenberg antiferromagnet and of the $J$-$Q$ model (with 4-spin interactions $Q$ and Heisenberg exchange $J$). Using an improved method for stochastic analytic continuation of imaginary-time correlation functions computed with QMC simulations, we can treat the sharp ($δ$-function) contribution from spinwaves (magnons) and a continuum at higher energy. The results for the Heisenberg model agree with neutron scattering experiments on Cu(DCOO)$_2$$\cdot$4D$_2$O, where a broad spectral-weight continuum at $q=(π,0)$ was interpreted as deconfined spinons. Our results at $(π,0)$ show a similar reduction of the magnon weight and a large continuum, while the continuum is much smaller at $q=(π/2,π/2)$ (as also seen experimentally). Turning on $Q$, we observe a rapid reduction of the $(π,0)$ magnon weight to zero, well before the deconfined quantum phase transition into a spontaneously dimerized state. We re-interpret the picture of deconfined spinons at $(π,0)$ in the experiments as nearly deconfined spinons---a precursor to deconfined quantum criticality. To further elucidate the picture of a fragile $(π,0)$-magnon in the Heisenberg model and its depletion in the $J$-$Q$ model, we introduce an effective model in which a magnon can split into two spinons that do not separate but fluctuate in and out of the magnon space (in analogy with the resonance between a photon and a particle-hole pair in the exciton-polariton problem). The model reproduces the $(π,0)$ and $(π/2,π/2)$ features of the Heisenberg model. It can also account for the rapid loss of the $(π,0)$ magnon with increasing $Q$ and a remarkable persistence of a large magnon pole at $q=(π/2,π/2)$ even at the deconfined critical point. △ Less

Submitted 23 November, 2017; v1 submitted 10 August, 2017; originally announced August 2017.

Comments: 25 pages, 24 figures, some additional discussion in version 3, to be appeared in PRX

Journal ref: Phys. Rev. X 7, 041072 (2017)

Competing Bose-Glass physics with disorder-induced Bose-Einstein condensation in the doped $S=1$ antiferromagnet Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ at high magnetic fields

Authors: Maxime Dupont, Sylvain Capponi, Mladen Horvatić, Nicolas Laflorencie

Abstract: We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ (DTNX). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization o… ▽ More We study the interplay between disorder and interactions for emergent bosonic degrees of freedom induced by an external magnetic field in the Br-doped spin-gapped antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ (DTNX). Building on nuclear magnetic resonance experiments at high magnetic field [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we describe the localization of isolated impurity states, providing a realistic theoretical modeling for DTNX. Going beyond single impurity localization we use quantum Monte Carlo simulations to explore many-body effects from which pairwise effective interactions lead to a (impurity-induced) BEC revival [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017)]. We further address the question of the existence of a many-body localized Bose-glass (BG) phase in DTNX, which is found to compete with a series of a new kind of BEC regimes made out of the multi-impurity states. The global magnetic field-temperature phase diagram of DTNX reveals a very rich structure for low impurity concentration, with consecutive disorder-induced BEC mini-domes separated by intervening many-body localized BG regimes. Upon increasing the impurity level, multiple mini-BEC phases start to overlap, while intermediate BG regions vanish. △ Less

Submitted 27 July, 2017; v1 submitted 19 May, 2017; originally announced May 2017.

Comments: 16 pages, 13 figures

Journal ref: Phys. Rev. B 96, 024442 (2017)

Weak Versus Strong Disorder Superfluid-Bose Glass Transition in One Dimension

Authors: Elmer V. H. Doggen, Gabriel Lemarié, Sylvain Capponi, Nicolas Laflorencie

Abstract: Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different re… ▽ More Using large-scale simulations based on matrix product state and quantum Monte Carlo techniques, we study the superfluid to Bose glass-transition for one-dimensional attractive hard-core bosons at zero temperature, across the full regime from weak to strong disorder. As a function of interaction and disorder strength, we identify a Berezinskii-Kosterlitz-Thouless critical line with two different regimes. At small attraction where critical disorder is weak compared to the bandwidth, the critical Luttinger parameter $K_c$ takes its universal Giamarchi-Schulz value $K_{c}=3/2$. Conversely, a non-universal $K_c>3/2$ emerges for stronger attraction where weak-link physics is relevant. In this strong disorder regime, the transition is characterized by self-similar power-law distributed weak links with a continuously varying characteristic exponent $α$. △ Less

Submitted 20 July, 2017; v1 submitted 7 April, 2017; originally announced April 2017.

Comments: 4+epsilon pages, 3 figures, 6-epsilon pages of supplementary material. Comments welcome

Journal ref: Phys. Rev. B 96, 180202 (2017)

Numerical study of magnetization plateaux in the spin-1/2 Heisenberg antiferromagnet on the checkerboard lattice

Authors: Sylvain Capponi

Abstract: We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible states correspond to somehow similar valence-bond crystal phases that break lattice symmetries, though they are different from the already… ▽ More We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible states correspond to somehow similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m=0. Our results are based on Exact Diagonalization as well as Density Matrix Renormalization Group large-scale simulations, and interpreted in terms of simple trial wavefunctions. △ Less

Submitted 24 January, 2017; v1 submitted 15 November, 2016; originally announced November 2016.

Comments: published version

Journal ref: Phys. Rev. B 95, 014420 (2017)

Disorder-induced Revival of the Bose-Einstein Condensation in Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ at High Magnetic Fields

Authors: Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie

Abstract: Building on recent NMR experiments [Phys. Rev. Lett. 118, 067203], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional $S=1$ antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond… ▽ More Building on recent NMR experiments [Phys. Rev. Lett. 118, 067203], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional $S=1$ antiferromagnetic material Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond the well-known antiferromagnetically ordered regime, analog of a Bose condensate of magnons, which disappears when $H\ge 12.3$ T, we unveil a resurgence of phase coherence at higher field $H\sim 13.6$ T, induced by the doping. Interchain couplings stabilize finite temperature long-range order whose extension in the field - temperature space is governed by the concentration of impurities $x$. Such a "mini-condensation" contrasts with previously reported Bose-glass physics in the same regime, and should be accessible to experiments. △ Less

Submitted 16 February, 2017; v1 submitted 17 October, 2016; originally announced October 2016.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. Lett. 118, 067204 (2017)

Nuclear magnetic resonance study of the magnetic-field-induced ordered phase in the NiCl2-4SC(NH2)2 compound

Authors: Rémi Blinder, Maxime Dupont, Sutirtha Mukhopadhyay, Mihael S. Grbić, Nicolas Laflorencie, Sylvain Capponi, Hadrien Mayaffre, Claude Berthier, Armando Paduan-Filho, Mladen Horvatić

Abstract: Nuclear magnetic resonance (NMR) study of the high magnetic field (H) part of the Bose-Einstein condensed (BEC) phase of the quasi-onedimensional (quasi-1D) antiferromagnetic quantum spin-chain compound NiCl2-4SC(NH2)2 (DTN) was performed. We precisely determined the phase boundary, Tc(H), down to 40 mK; the critical boson density, n_c(Tc); and the absolute value of the BEC order parameter S_perp… ▽ More Nuclear magnetic resonance (NMR) study of the high magnetic field (H) part of the Bose-Einstein condensed (BEC) phase of the quasi-onedimensional (quasi-1D) antiferromagnetic quantum spin-chain compound NiCl2-4SC(NH2)2 (DTN) was performed. We precisely determined the phase boundary, Tc(H), down to 40 mK; the critical boson density, n_c(Tc); and the absolute value of the BEC order parameter S_perp at very low temperature (T = 0.12 K). All results are accurately reproduced by numerical quantum Monte Carlo simulations of a realistic three-dimensional (3D) model Hamiltonian. Approximate analytical predictions based on the 1D Tomonaga-Luttinger liquid description are found to be precise for Tc(H), but less so for S_perp(H), which is more sensitive to the strength of 3D couplings, in particular close to the critical field. A mean-field treatment, based on the Hartree-Fock-Popov description, is found to be valid only up to n_c = 4% (T < 0.3 K), while for higher n_c boson interactions appear to modify the density of states. △ Less

Submitted 9 February, 2017; v1 submitted 11 October, 2016; originally announced October 2016.

Comments: Manuscript (6 pages, 3 figures) and the corresponding Supplemental material (5 pages, 6 figures), altogether 11 pages and 9 figures

Journal ref: Phys. Rev. B 95, 020404(R) (2017)

Phase diagram of interacting spinless fermions on the honeycomb lattice

Authors: Sylvain Capponi

Abstract: Fermions hopping on a hexagonal lattice represent one of the most active research field in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and quantum mechanical effects is given by the Haldane model (F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)) where spinless fermions experiencing a certain fl… ▽ More Fermions hopping on a hexagonal lattice represent one of the most active research field in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and quantum mechanical effects is given by the Haldane model (F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)) where spinless fermions experiencing a certain flux pattern on the honeycomb lattice leads to the stabilization of a topological phase of matter, distinct from a Mott insulator and dubbed Chern insulator nowadays. In this context, it is crucial to understand the role of interactions and this review will describe recent results that have been obtained for a minimal model, namely spinless fermions fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Topics addressed include an introduction of the minimal model and a discussion of the possible instabilities of the Dirac semimetal, a presentation of various theroretical and numerical approaches, and a summary of the results with a particular emphasis on the stability or not of some exotic quantum phases such as charge ordered ones (similar to Wigner crystals) or spontaneous Chern insulator phase. △ Less

Submitted 28 November, 2016; v1 submitted 5 September, 2016; originally announced September 2016.

Comments: Published version with minor changes

Journal ref: J. Phys.: Condens. Matter 29 (2017) 043002

Staircase of crystal phases of hard-core bosons on the Kagome lattice

Authors: Daniel Huerga, Sylvain Capponi, Jorge Dukelsky, Gerardo Ortiz

Abstract: We study the quantum phase diagram of a system of hard-core bosons on the Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean field theory and exact diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In… ▽ More We study the quantum phase diagram of a system of hard-core bosons on the Kagome lattice with nearest-neighbor repulsive interactions, for arbitrary densities, by means of the hierarchical mean field theory and exact diagonalization techniques. This system is isomorphic to the spin S=1/2 XXZ model in presence of an external magnetic field, a paradigmatic example of frustrated quantum magnetism. In the non-frustrated regime, we find two crystal phases at densities 1/3 and 2/3 that melt into a superfluid phase when increasing the hopping amplitude, in semi-quantitative agreement with quantum Monte Carlo computations. In the frustrated regime and away from half-filling, we find a series of plateaux with densities commensurate with powers of 1/3. The broader density plateaux (at densities 1/3 and 2/3) are remnants of the classical degeneracy in the Ising limit. For densities near half-filling, this staircase of crystal phases melts into a superfluid, which displays finite chiral currents when computed with clusters having an odd number of sites. Both the staircase of crystal phases and the superfluid phase prevail in the non-interacting limit, suggesting that the lowest dispersionless single-particle band may be at the root of this phenomenon. △ Less

Submitted 14 October, 2016; v1 submitted 25 July, 2016; originally announced July 2016.

Journal ref: Phys. Rev. B 94, 165124 (2016)

Dimensional modulation of spontaneous magnetic order in quasi-two-dimensional quantum antiferromagnets

Authors: Shunsuke C. Furuya, Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie, Thierry Giamarchi

Abstract: Spontaneous symmetry breaking is deeply related to dimensionality of system. The Neel order going with spontaneous breaking of $U(1)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero temperature for purely two-dimensional systems. We closely investigate how smoothly the ordering process of the three-dimensional system is modulated into that of th… ▽ More Spontaneous symmetry breaking is deeply related to dimensionality of system. The Neel order going with spontaneous breaking of $U(1)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero temperature for purely two-dimensional systems. We closely investigate how smoothly the ordering process of the three-dimensional system is modulated into that of the two-dimensional one with reduction of dimensionality, considering spatially anisotropic quantum antiferromagnets. We first show that the Néel temperature is kept finite even in the two-dimensional limit although the Néel order is greatly suppressed for low-dimensionality. This feature of the Néel temperature is highly nontrivial, which dictates how the order parameter is squashed under the reduction of dimensionality. Next we investigate this dimensional modulation of the order parameter. We develop our argument taking as example a coupled spin-ladder system relevant for experimental studies. The ordering process is investigated multidirectionally using theoretical techniques of a mean-field method combined with analytical (exact solutions of quantum field theories) or numerial (density-matrix renormalization-group) method, a variational method, a renormalization-group study, linear spin-wave theory, and quantum Monte-Carlo simulation. We show that these methods independent of each other lead to the same conclusion about the dimensional modulation. △ Less

Submitted 3 October, 2016; v1 submitted 18 July, 2016; originally announced July 2016.

Journal ref: Phys. Rev. B 94, 144403 (2016)

Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-doped Ni(Cl$_{1-x}$Br$_x$)$_2$-4SC(NH$_2$)$_2$ Compound at a High Magnetic Field

Authors: Anna Orlova, Rémi Blinder, Edwin Kermarrec, Maxime Dupont, Nicolas Laflorencie, Sylvain Capponi, Hadrien Mayaffre, Claude Berthier, Armando Paduan-Filho, Mladen Horvatić

Abstract: By measuring the nuclear magnetic resonance (NMR) 1/T_1 relaxation rate in the Br (bond) doped DTN compound, Ni(Cl(1-x)Br_x)2-4SC(NH2)2 (DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H* = 13.6 T. From its temperature and field dependence we conclude t… ▽ More By measuring the nuclear magnetic resonance (NMR) 1/T_1 relaxation rate in the Br (bond) doped DTN compound, Ni(Cl(1-x)Br_x)2-4SC(NH2)2 (DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H* = 13.6 T. From its temperature and field dependence we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017), arXiv:1610.05136]. △ Less

Submitted 10 February, 2017; v1 submitted 8 July, 2016; originally announced July 2016.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. Lett. 118, 067203 (2017)

Temperature dependence of the NMR relaxation rate 1/T_1 for quantum spin chains

Authors: Maxime Dupont, Sylvain Capponi, Nicolas Laflorencie

Abstract: We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix Product States (MPS) formalism, we can follow the non-trivial crossover occurring in critical chains between the high-temperature diffusive classical regime an… ▽ More We present results of numerical simulations performed on one-dimensional spin chains in order to extract the so-called relaxation rate $1/T_1$ accessible through NMR experiments. Building on numerical tensor network methods using the Matrix Product States (MPS) formalism, we can follow the non-trivial crossover occurring in critical chains between the high-temperature diffusive classical regime and the low-temperature response described by the Tomonaga-Luttinger liquid (TLL) theory, for which analytical expressions are known. In order to compare analytics and numerics, we focus on a generic spin-$1/2$ XXZ chain which is a paradigm of gapless TLL, as well as a more realistic spin-$1$ anisotropic chain, modelling the DTN material, which can be either in a trivial gapped phase or in a TLL regime induced by an external magnetic field. Thus, by monitoring the finite temperature crossover, we provide quantitative limits on the range of validity of TLL theory, that will be useful when interpreting experiments on quasi one-dimensional materials. △ Less

Submitted 13 October, 2016; v1 submitted 30 June, 2016; originally announced June 2016.

Comments: 12 pages, 6 figures

Journal ref: Phys. Rev. B 94, 144409 (2016)

Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases

Authors: S. Capponi, P. Lecheminant, K. Totsuka

Abstract: Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry- protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of… ▽ More Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry- protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multicomponent Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N > 2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N-particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states. △ Less

Submitted 28 February, 2016; v1 submitted 15 September, 2015; originally announced September 2015.

Comments: 59 pages, 20 figures. Review article published in Annals of Physics. Some minor errors fixed

Journal ref: Ann.Phys. 367, 50 (2016)

Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice

Authors: Matthieu Mambrini, Sylvain Capponi, Fabien Alet

Abstract: We consider the spin-1/2 hamiltonians proposed by Cano and Fendley [J. Cano and P. Fendley, Phys. Rev. Lett. 105, 067205 (2010)] which were built to promote the well-known Rokshar-Kivelson (RK) point of quantum dimer models to spin-1/2 wavefunctions. We first show that these models, besides the exact degeneracy of RK point, support gapless spinless excitations as well as a spin gap in the thermody… ▽ More We consider the spin-1/2 hamiltonians proposed by Cano and Fendley [J. Cano and P. Fendley, Phys. Rev. Lett. 105, 067205 (2010)] which were built to promote the well-known Rokshar-Kivelson (RK) point of quantum dimer models to spin-1/2 wavefunctions. We first show that these models, besides the exact degeneracy of RK point, support gapless spinless excitations as well as a spin gap in the thermodynamic limit, signatures of an unusual spin liquid. We then extend the original construction to create a continuous family of SU(2) invariant spin models that reproduces the phase diagram of the quantum dimer model, and in particular show explicit evidences for existence of columnar and staggered phases. The original models thus appear as multicritical points in an extended phase diagram. Our results are based on the use of a combination of numerical exact simulations and analytical mapping to effective generalized quantum dimer models. △ Less

Submitted 20 October, 2015; v1 submitted 28 July, 2015; originally announced July 2015.

Comments: 12 pages, 8 figures

Journal ref: Phys. Rev. B 92, 134413 (2015)

Magnetization plateaus of an easy-axis Kagomé antiferromagnet with extended interactions

Authors: X. Plat, F. Alet, S. Capponi, K. Totsuka

Abstract: We investigate the properties in finite magnetic field of an extended anisotropic XXZ spin-1/2 model on the Kagome lattice, originally introduced by Balents, Fisher, and Girvin [Phys. Rev. B, 65, 224412 (2002)]. The magnetization curve displays plateaus at magnetization m=1/6 and 1/3 when the anisotropy is large. Using low-energy effective constrained models (quantum loop and quantum dimer models)… ▽ More We investigate the properties in finite magnetic field of an extended anisotropic XXZ spin-1/2 model on the Kagome lattice, originally introduced by Balents, Fisher, and Girvin [Phys. Rev. B, 65, 224412 (2002)]. The magnetization curve displays plateaus at magnetization m=1/6 and 1/3 when the anisotropy is large. Using low-energy effective constrained models (quantum loop and quantum dimer models), we discuss the nature of the plateau phases, found to be crystals that break discrete rotation and/or translation symmetries. Large-scale quantum Monte-Carlo simulations were carried out in particular for the m=1/6 plateau. We first map out the phase diagram of the effective quantum loop model with an additional loop-loop interaction to find stripe order around the point relevant for the original model as well as a topological Z2 spin liquid. The existence of a stripe crystalline phase is further evidenced by measuring both standard structure factor and entanglement entropy of the original microscopic model. △ Less

Submitted 8 November, 2015; v1 submitted 29 May, 2015; originally announced May 2015.

Comments: 14 pages, 14 figures

Journal ref: Phys. Rev. B 92, 174402 (2015)

Competing superconducting instabilities in the one-dimensional p-band degenerate cold fermionic system

Authors: V. Bois, S. Capponi, P. Lecheminant, M. Moliner

Abstract: The zero-temperature phase diagram of $p$-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the $p$-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter filling, we analyze the possible formation of inco… ▽ More The zero-temperature phase diagram of $p$-orbital two-component fermionic system loaded into a one-dimensional optical lattice is mapped out by means of analytical and numerical techniques. It is shown that the $p$-band model away from half-filling hosts various competing superconducting phases for attractive and repulsive interactions. At quarter filling, we analyze the possible formation of incompressible Mott phases and in particular for repulsive interactions, we find the occurrence of a Mott transition with the formation of fully gapped bond-ordering waves. △ Less

Submitted 27 August, 2015; v1 submitted 25 May, 2015; originally announced May 2015.

Comments: published version

Journal ref: Phys. Rev. B 92, 075140 (2015)

Phase diagram of interacting spinless fermions on the honeycomb lattice: A comprehensive exact diagonalization study

Authors: Sylvain Capponi, Andreas M. Läuchli

Abstract: We investigate the phase diagram of spinless fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Using Exact Diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this re… ▽ More We investigate the phase diagram of spinless fermions with nearest and next-nearest neighbour density-density interactions on the honeycomb lattice at half-filling. Using Exact Diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this regime we find a two-sublattice Néel-like state, a charge modulated state with a tripling of the unit cell, a zig-zag phase and a novel charge ordered states with a 12 site unit cells we call Néel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizeable region of the phase diagram is classically degenerate, but it remains unclear whether an order-by-disorder mechanism will lift the degeneracy. For intermediate repulsion we find evidence for a Kekulé or plaquette bond-order wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several mean-field studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of current-current correlations with the expected spatial structure compared to the non-interacting situation. While for the studied $t{-}V_1{-}V_2$ model the phase transition to the putative topological Mott insulator is preempted by the phase transitions to the various ordered states, our findings might hint at the possibility for a topological Mott insulator in an enlarged Hamiltonian parameter space, where the competing phases are suppressed. △ Less

Submitted 27 August, 2015; v1 submitted 7 May, 2015; originally announced May 2015.

Comments: published version

Journal ref: Phys. Rev. B 92, 085146 (2015)