Showing 1–45 of 45 results for author: Strand, H U R

Strong correlations and local self-energies from on-site ensembles

Authors: Alberto Carta, Hugo U. R. Strand, Michael Schüler, Nicola Marzari

Abstract: Addressing the many-body electronic-structure problem is a central goal of modern condensed-matter physics. Paramagnetic Mott insulators, in particular, have long represented a challenge for standard approaches, such as density-functional theory. Historically, these systems have been tackled either by considering many-body dynamics, as in the case of dynamical mean-field theory (DMFT), or, more re… ▽ More Addressing the many-body electronic-structure problem is a central goal of modern condensed-matter physics. Paramagnetic Mott insulators, in particular, have long represented a challenge for standard approaches, such as density-functional theory. Historically, these systems have been tackled either by considering many-body dynamics, as in the case of dynamical mean-field theory (DMFT), or, more recently, by invoking a polymorphous description consisting of large supercells populated with static symmetry-broken motifs whose spatial average restores the paramagnetic state. Inspired by these viewpoints, we introduce the on-site dephased ensemble (DE) approximation, in which the local electronic-structure problem is described by a thermal ensemble of all accessible local static solutions; this gives rise to a strong frequency dependence of the local electronic self-energy, as seen in DMFT or in the coherent-potential approximation of disordered alloys. We show that the DE successfully recovers defining hallmarks of strongly correlated Mott systems, both in terms of the self-energy as well as the persistence of local moments in time, in quantitative agreement with DMFT. By bypassing expensive quantum Monte Carlo solvers or large supercell calculations, this approach offers efficient routes to treating paramagnetic Mott systems in a first-principles setting, and highlights a deeper connection between the physics of strong correlations and that of disorder. △ Less

Submitted 23 July, 2026; originally announced July 2026.

Benchmarking the Dual Fermion approach on the Falicov-Kimball model

Authors: Akshat Mishra, Hugo U. R. Strand, Erik G. C. P. van Loon

Abstract: Strong electronic correlations generally require non-perturbative treatment. Local correlations are captured by dynamical mean-field theory while nonlocal correlations can be treated with diagrammatic extensions such as the Dual Fermion approach. Dual Fermion is built on physically motivated, but in principle uncontrolled approximations, so careful benchmarking is needed to understand the strength… ▽ More Strong electronic correlations generally require non-perturbative treatment. Local correlations are captured by dynamical mean-field theory while nonlocal correlations can be treated with diagrammatic extensions such as the Dual Fermion approach. Dual Fermion is built on physically motivated, but in principle uncontrolled approximations, so careful benchmarking is needed to understand the strengths and limitations of the method. In this work, we benchmark ladder Dual Fermion and dynamical mean-field theory for the Falicov-Kimball model with the exact classical Monte Carlo solution. We focus on the thermodynamics, electronic structure and susceptibility, especially at the combined frequency and momentum structure, and find that Dual Fermion clearly outperforms dynamical mean-field theory. Somewhat surprisingly, Dual Fermion is not as accurate for the relation between orbital density versus chemical potential in the doped system. These results demonstrate the need for rigorous benchmarking of diagrammatic extensions of dynamical mean-field theory for models with inequivalent orbitals, which is essential for modelling materials. △ Less

Submitted 4 May, 2026; originally announced May 2026.

NESSi 2.0: The Non-Equilibrium Systems Simulation package version 2.0

Authors: Fabian Künzel, Michael Schüler, Denis Golež, Yuta Murakami, Sujay Ray, Christopher Stahl, Jiajun Li, Hugo U. R. Strand, Philipp Werner, Martin Eckstein

Abstract: Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for such simulations, ranging from perturbative approaches like nonequilibrium $GW$ to nonequilibrium dynamical mean-field theory. However, simulations based on noneq… ▽ More Nonequilibrium Green's functions provide a powerful framework for studying quantum many-body dynamics including the laser-induced dynamics in solids. The Non-Equilibrium Systems Simulation package (NESSi) offers an efficient platform for such simulations, ranging from perturbative approaches like nonequilibrium $GW$ to nonequilibrium dynamical mean-field theory. However, simulations based on nonequilibrium Green's functions become computationally demanding when the dynamics span a large temporal range, such as from sub-femtosecond electron dynamics to the picosecond dynamics of collective modes. Due to the memory integral in the Kadanoff-Baym equations, which serve as equations of motion for nonequilibrium Green's functions, the computational cost scales as $\mathcal{O}(N_t^3)$ with the number of timesteps $N_t$, and the memory requirement scales as $\mathcal{O}(N_t^2)$. In this work, we extend NESSi by incorporating techniques that aim to overcome this bottleneck: (i) By truncating the memory integrals in the KBE to a maximum of $N_c$ timesteps, the computational complexity is reduced to $\mathcal{O}(N_tN_c^2)$, and the memory requirement to $\mathcal{O}(N_c^2)$. Provided that the results converge with respect to the cutoff $N_c$, memory truncation allows to extend the simulations to significantly longer times. (ii) We introduce functionalities to describe nonequilibrium steady states, i.e. time-translationally invariant nonequilibrium states. Such states are relevant for transport settings, and they provide an approximate description of slowly evolving (prethermal) nonequilibrium states. △ Less

Submitted 4 May, 2026; originally announced May 2026.

Comments: 45 pages, 11 figures

Open Quantum Cluster Embedding Theory

Authors: Petar Brinić, Hugo U. R. Strand, Jakša Vučičević

Abstract: The simulation of strongly correlated electron systems remains a formidable challenge. Certain experimentally relevant dynamical response functions are especially difficult to calculate, due to issues of finite-size effects and the ill posed analytic continuation. To address this we propose the quantum cluster embedding theory, an embedded cluster method aimed at computing the response of the syst… ▽ More The simulation of strongly correlated electron systems remains a formidable challenge. Certain experimentally relevant dynamical response functions are especially difficult to calculate, due to issues of finite-size effects and the ill posed analytic continuation. To address this we propose the quantum cluster embedding theory, an embedded cluster method aimed at computing the response of the system following an external perturbation; the frequency dependent dynamical susceptibility is obtained subsequently by means of inverse linear response theory. The embedded clusters, used within the method as representative of short range correlations, are open quantum systems governed by the Lindblad equation. The short-range correlations extracted from the clusters are used to close the equations of motion for the fermionic bilinear and the local double occupancy on the lattice. In turn, the clusters' Markovian baths are tuned to keep the bilinear and the double occupancy expectation values on the clusters and the lattice identical, throughout the concomitant evolution of the two sets of equations. The theory becomes numerically exact in the non-interacting, atomic and infinite cluster size limits, and it respects the total charge and energy conservation laws. We show that our approach can treat very large lattices while avoiding analytic continuation through the explicit time evolution. Finally we compute the charge-charge correlation function in the square lattice Hubbard model and compare with a recent cold atom experiment, finding good qualitative agreement. △ Less

Submitted 24 March, 2026; originally announced March 2026.

Comments: 30 pages, 27 figures

Magnons in multiorbital Hubbard models, from Lieb to kagome

Authors: Teng-Fei Ying, Hugo U. R. Strand, Benjamin T. Zhou, Erik G. C. P. van Loon

Abstract: We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using self-consistent Hartree-Fock approximation combined with real-time two-particle response functions from the Bethe-Salpeter equation in the random phase approximation, we map the $U-t'$ phase diagram of the Lieb-kagome lattices, identifying the… ▽ More We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using self-consistent Hartree-Fock approximation combined with real-time two-particle response functions from the Bethe-Salpeter equation in the random phase approximation, we map the $U-t'$ phase diagram of the Lieb-kagome lattices, identifying the typical magnetic states and the corresponding magnetic excitation spectra. In addition to gapless Goldstone magnons, the ferrimagnetic and antiferromagnetic symmetry-broken phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking. △ Less

Submitted 18 January, 2026; v1 submitted 12 January, 2026; originally announced January 2026.

Real-space first-principles approach to orbitronic phenomena in metallic multilayers

Authors: Ramon Cardias, Hugo U. R. Strand, Anders Bergman, A. B. Klautau, Tatiana G. Rappoport

Abstract: We develop a real-space first-principles method based on density functional theory to investigate orbitronic phenomena in complex materials. Using the Real-Space Linear Muffin-Tin Orbital method within the Atomic Sphere Approximation (RS-LMTO-ASA) combined with a Chebyshev polynomial expansion of the Green's functions, we compute orbital (spin) Hall transport and orbital (spin) accumulation direct… ▽ More We develop a real-space first-principles method based on density functional theory to investigate orbitronic phenomena in complex materials. Using the Real-Space Linear Muffin-Tin Orbital method within the Atomic Sphere Approximation (RS-LMTO-ASA) combined with a Chebyshev polynomial expansion of the Green's functions, we compute orbital (spin) Hall transport and orbital (spin) accumulation directly in real space. The approach scales linearly with system size and naturally incorporates disorder, finite-size effects, and interface roughness. We apply the method to transition-metal-based heterostructures and demonstrate the emergence of substantial orbital (spin) accumulation, even in centrosymmetric systems. Our methodology provides a scalable and flexible framework for realistic simulations of orbital transport phenomena in complex heterostructures. △ Less

Submitted 19 August, 2025; originally announced August 2025.

Comments: 12 pages, 5 figures

Journal ref: Communication Physics 2026, 9, Article number: 203 (2026)

Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model

Authors: Nagamalleswararao Dasari, Hugo U. R. Strand, Martin Eckstein, Alexander I. Lichtenstein, Evgeny A. Stepanov

Abstract: Conductivity is one of the most direct probes of electronic systems, yet its theoretical description remains challenging in the presence of strong non-local correlations. In this Letter, we analyze the conductivity of the half-filled single-band Hubbard model and identify the role of spatial correlations across the Mott transition. We show that in the correlated metallic regime, an accurate descri… ▽ More Conductivity is one of the most direct probes of electronic systems, yet its theoretical description remains challenging in the presence of strong non-local correlations. In this Letter, we analyze the conductivity of the half-filled single-band Hubbard model and identify the role of spatial correlations across the Mott transition. We show that in the correlated metallic regime, an accurate description of the conductivity requires not only the correct spectral function but also the inclusion of complex multi-electron processes encoded in vertex corrections. The crossover to the Mott insulating regime is marked by a vanishing contribution of vertex corrections to the DC conductivity. However, in the Mott insulating case, vertex corrections remain significant for the optical conductivity. △ Less

Submitted 12 March, 2026; v1 submitted 22 July, 2025; originally announced July 2025.

Comments: 14 pages, 9 figures

Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study

Authors: Nagamalleswararao Dasari, Hugo U. R. Strand, Martin Eckstein, Alexander I. Lichtenstein, Evgeny A. Stepanov

Abstract: Ultrafast irradiation of correlated electronic systems triggers complex dynamics involving quasi-particle excitations, doublons, charge carriers, and spin fluctuations. To describe these effects, we develop an efficient non-equilibrium approach, dubbed D-$GW$, that enables a self-consistent treatment of local correlations within dynamical mean-field theory (DMFT) and spatial charge and spin fluctu… ▽ More Ultrafast irradiation of correlated electronic systems triggers complex dynamics involving quasi-particle excitations, doublons, charge carriers, and spin fluctuations. To describe these effects, we develop an efficient non-equilibrium approach, dubbed D-$GW$, that enables a self-consistent treatment of local correlations within dynamical mean-field theory (DMFT) and spatial charge and spin fluctuations, that are accounted for simultaneously within a diagrammatic framework. The method is formulated in the real-time domain and provides direct access to single- and two-particle momentum- and energy-dependent response functions without the need for analytical continuation, which is required in Matsubara frequency-based approaches. We apply the D-$GW$ method to investigate the dynamics of a photo-excited extended Hubbard model, the minimal system that simultaneously hosts strong charge and spin fluctuations. Focusing on the challenging parameter regime near the Mott transition, we demonstrate that correlated metals and narrow-gap Mott insulators undergo distinct thermalization processes involving complex energy transfer between single-particle and collective electronic excitations. △ Less

Submitted 7 April, 2025; originally announced April 2025.

Comments: 21 pages, 13 figures

Journal ref: Phys. Rev. B 111, 235129 (2025)

Driving collective current excitations using light: The two-time $GW$ approach

Authors: Chin Shen Ong, Denis Golež, Angel Rubio, Olle Eriksson, Hugo U. R. Strand

Abstract: We identify a distinct transverse collective excitation, which we name the "curron", arising from current-current interactions in a driven quantum metal. Unlike plasmons, which involve longitudinal charge oscillations, currons are transverse current-density oscillations resulting from the interplay between the vector potential generated by the current and the external driving field. We demonstrate… ▽ More We identify a distinct transverse collective excitation, which we name the "curron", arising from current-current interactions in a driven quantum metal. Unlike plasmons, which involve longitudinal charge oscillations, currons are transverse current-density oscillations resulting from the interplay between the vector potential generated by the current and the external driving field. We demonstrate the emergence of this excitation in sodium metal by solving the Kadanoff-Baym equations on a complex time contour within the non-equilibrium two-time (TT) $GW$ formalism, marking, to our knowledge, the first TT-$GW$ calculation on a realistic material. We further show that two-time quantum memory effects leave measurable signatures: a pump-induced elevation in the baseline of the current-to-field response, potentially observable in polarization- and momentum-resolved conductivity experiments. By extracting effective resistive and memory coefficients from the TT-$GW$ dynamics, we introduce a generalized d'Alembert wave equation that captures the many-body damping and retardation inherent to driven quantum systems. These results establish current-current response functions as a platform to harness qualitatively new collective dynamics in correlated matter, opening new avenues for probing light-matter interactions beyond charge-density dynamics. △ Less

Submitted 17 July, 2025; v1 submitted 1 April, 2025; originally announced April 2025.

Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting

Authors: Zhen Huang, Denis Golež, Hugo U. R. Strand, Jason Kaye

Abstract: We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting method based on AAA rational approximation and numerical optimization to obtain a sum-of-exponentials expansion of the hybridization function, which is then used t… ▽ More We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting method based on AAA rational approximation and numerical optimization to obtain a sum-of-exponentials expansion of the hybridization function, which is then used to decompose the diagrams. A diagrammatic formulation of the algorithm leads to an automated procedure for diagrams of arbitrary order and topology. We also present methods of stabilizing the self-consistent solution of the pseudo-particle Dyson equation. The result is a low-cost and high-order accurate impurity solver for quantum embedding methods using general multi-orbital hybridization functions at low temperatures, appropriate for low-to-intermediate expansion orders. In addition to other benchmark examples, we use our solver to perform a dynamical mean-field theory study of a minimal model of the strongly correlated compound Ca$_2$RuO$_4$, describing the anti-ferromagnetic transition and the in- and out-of-plane anisotropy induced by spin-orbit coupling. △ Less

Submitted 23 September, 2025; v1 submitted 25 March, 2025; originally announced March 2025.

Comments: 22 pages. 7 figures

Journal ref: SciPost Phys. 19, 121 (2025)

Edge non-collinear magnetism in nanoribbons of Fe3GeTe2 and Fe3GaTe2

Authors: R. Cardias, Anders Bergman, Hugo U. R. Strand, R. B. Muniz, Marcio Costa

Abstract: Fe3GeTe2 and Fe3GaTe2 are ferromagnetic conducting materials of van der Waals-type with unique magnetic properties that are highly promising for the development of new spintronic, orbitronic and magnonic devices. Even in the form of two-dimensional-like ultrathin films, they exhibit relatively high Curie temperature, magnetic anisotropy perpendicular to the atomic planes and multiple types of Hall… ▽ More Fe3GeTe2 and Fe3GaTe2 are ferromagnetic conducting materials of van der Waals-type with unique magnetic properties that are highly promising for the development of new spintronic, orbitronic and magnonic devices. Even in the form of two-dimensional-like ultrathin films, they exhibit relatively high Curie temperature, magnetic anisotropy perpendicular to the atomic planes and multiple types of Hall effects. We explore nanoribbons made from single layers of these materials and show that they display non-collinear magnetic ordering at their edges. This magnetic inhomogeneity allows angular momentum currents to generate magnetic torques at the sample edges, regardless of their polarization direction, significantly enhancing the effectiveness of magnetization manipulation in these systems. We also demonstrate that it is possible to rapidly reverse the magnetization direction of these nanostructures by means of spin-orbit and spin-transfer torques with rather low current densities, making them quite propitious for non-volatile magnetic memory units. △ Less

Submitted 17 February, 2025; originally announced February 2025.

Comments: 5 pages, 4 figures

Journal ref: Nano Lett. 25, 31, 11797-11802 (2025)

From strong to weak correlations in breathing-mode kagome van der Waals materials: Nb$_3$(F,Cl,Br,I)$_8$ as a robust and versatile platform for many-body engineering

Authors: Joost Aretz, Sergii Grytsiuk, Xiaojing Liu, Giovanna Feraco, Chrystalla Knekna, Muhammad Waseem, Zhiying Dan, Marco Bianchi, Philip Hofmann, Mazhar N. Ali, Mikhail I. Katsnelson, Antonija Grubišić-Čabo, Hugo U. R. Strand, Erik G. C. P. van Loon, Malte Rösner

Abstract: By combining ab initio downfolding with cluster dynamical mean-field theory, we study the degree of correlations in monolayer, bilayer and bulk breathing-mode kagome van der Waals materials Nb$_3$(F,Cl,Br,I)$_8$. Our new material-specific many-body model library shows that in low-temperature bulk structures the Coulomb correlation strength steadily increases from I to F, allowing us to identify Nb… ▽ More By combining ab initio downfolding with cluster dynamical mean-field theory, we study the degree of correlations in monolayer, bilayer and bulk breathing-mode kagome van der Waals materials Nb$_3$(F,Cl,Br,I)$_8$. Our new material-specific many-body model library shows that in low-temperature bulk structures the Coulomb correlation strength steadily increases from I to F, allowing us to identify Nb$_3$I$_8$ as a weakly correlated insulator, Nb$_3$Br$_8$ and Nb$_3$Cl$_8$ as strongly correlated insulators, and Nb$_3$F$_8$ as a prototypical bulk Mott-insulator. Angle-resolved photoemission spectroscopy measurements comparing Nb$_3$Br$_8$ and Nb$_3$I$_8$ allow us to experimentally confirm these findings by revealing spectroscopic footprints of the degree of correlation. Our calculations uncover how the thickness and the stacking affect the degree of correlations and predict that the entire material family can be tuned into correlated charge-transfer or Mott-insulating phases upon doping. Our magnetic property analysis based on our model parameter library additionally confirms that inter-layer magnetic interactions drive the lattice phase transition to the low-temperature structures. The accompanying bilayer hybridization through inter-layer dimerization yields magnetic singlet-like ground states in the Cl, Br, and I compounds. We further prove that all low-temperature compounds are dynamically stable and that electron-phonon coupling to the low-energy subspace is suppressed. Our findings establish Nb$_3$X$_8$ as a robust, versatile, and tunable class for van der Waals-based Coulomb and Mott engineering with a rich phase diagram and allow us to speculate on the symmetry-breaking effects necessary for the recently observed Josephson diode effect in NbSe$_2$/Nb$_3$Br$_8$/NbSe$_2$ heterostructures. △ Less

Submitted 22 August, 2025; v1 submitted 17 January, 2025; originally announced January 2025.

Comments: 39 pages, 25 figures

Journal ref: Phys. Rev. X 15, 041042 (2025)

Discrete Lehmann representation of three-point functions

Authors: Dominik Kiese, Hugo U. R. Strand, Kun Chen, Nils Wentzell, Olivier Parcollet, Jason Kaye

Abstract: We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We prese… ▽ More We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint. △ Less

Submitted 18 July, 2024; v1 submitted 9 May, 2024; originally announced May 2024.

Journal ref: Phys. Rev. B 111, 035135 (2025)

cppdlr: Imaginary time calculations using the discrete Lehmann representation

Authors: Jason Kaye, Hugo U. R. Strand, Nils Wentzell

Abstract: We introduce cppdlr, a C++ library implementing the discrete Lehmann representation (DLR) of functions in imaginary time and Matsubara frequency, such as Green's functions and self-energies. The DLR is based on a low-rank approximation of the analytic continuation kernel, and yields a compact and explicit basis consisting of exponentials in imaginary time and simple poles in Matsubara frequency. c… ▽ More We introduce cppdlr, a C++ library implementing the discrete Lehmann representation (DLR) of functions in imaginary time and Matsubara frequency, such as Green's functions and self-energies. The DLR is based on a low-rank approximation of the analytic continuation kernel, and yields a compact and explicit basis consisting of exponentials in imaginary time and simple poles in Matsubara frequency. cppdlr constructs the DLR basis and associated interpolation grids, and implements standard operations. It provides a flexible yet high-level interface, facilitating the incorporation of the DLR into both small-scale applications and existing large-scale software projects. △ Less

Submitted 2 April, 2024; originally announced April 2024.

MSC Class: 81-04; 65D15 ACM Class: G.4; J.2; G.1.2

Inchworm quasi Monte Carlo for quantum impurities

Authors: Hugo U. R. Strand, Joseph Kleinhenz, Igor Krivenko

Abstract: The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as $1/\sqrt{N}$ where $N$ is the number of samples. We show that the imaginary time integration is amenable to quasi Monte Carlo, with enhanced $1/N$ converge… ▽ More The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as $1/\sqrt{N}$ where $N$ is the number of samples. We show that the imaginary time integration is amenable to quasi Monte Carlo, with enhanced $1/N$ convergence, by mapping the Sobol low-discrepancy sequence from the hypercube to the simplex with the so-called Root transform. This extends the applicability of the inchworm method to, e.g., multi-orbital Anderson impurity models with off-diagonal hybridization, relevant for materials simulation, where continuous time hybridization expansion Monte Carlo has a severe sign problem. △ Less

Submitted 25 October, 2023; originally announced October 2023.

Journal ref: Phys. Rev. B 110, L121120 (2024)

Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion

Authors: Jason Kaye, Zhen Huang, Hugo U. R. Strand, Denis Golež

Abstract: We present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary time, allowing us to decompose diagrams into li… ▽ More We present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an $M$th-order diagram at inverse temperature $β$ and spectral width $ω_{\max}$ from $\mathcal{O}((βω_{\max})^{2M-1})$ for a direct quadrature to $\mathcal{O}(M (\log (βω_{\max}))^{M+1})$, with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multi-band impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca$_2$RuO$_4$, demonstrating the promise of the method for modeling realistic strongly correlated multi-band materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust black-box evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams. △ Less

Submitted 6 June, 2024; v1 submitted 17 July, 2023; originally announced July 2023.

Journal ref: Phys. Rev. X 14, 031034 (2024)

Dual Bethe-Salpeter equation for the multi-orbital lattice susceptibility within dynamical mean-field theory

Authors: Erik G. C. P. van Loon, Hugo U. R. Strand

Abstract: Dynamical mean-field theory describes the impact of strong local correlation effects in many-electron systems. While the single-particle spectral function is directly obtained within the formalism, two-particle susceptibilities can also be obtained by solving the Bethe-Salpeter equation. The solution requires handling infinite matrices in Matsubara frequency space. This is commonly treated using a… ▽ More Dynamical mean-field theory describes the impact of strong local correlation effects in many-electron systems. While the single-particle spectral function is directly obtained within the formalism, two-particle susceptibilities can also be obtained by solving the Bethe-Salpeter equation. The solution requires handling infinite matrices in Matsubara frequency space. This is commonly treated using a finite frequency cut-off, resulting in slow linear convergence. A decomposition of the two-particle response in local and non-local contributions enables a reformulation of the Bethe-Salpeter equation inspired by the dual boson formalism. The re-formulation has a drastically improved cubic convergence with respect to the frequency cut-off, facilitating the calculation of susceptibilities in multi-orbital systems considerably. This improved convergence arises from the fact that local contributions can be measured in the impurity solver. The dual Bethe-Salpeter equation uses the fully reducible vertex which is free from vertex divergences. We benchmark the approach on several systems including the spin susceptibility of strontium ruthenate Sr$_2$RuO$_4$, a strongly correlated Hund's metal with three active orbitals. △ Less

Submitted 15 May, 2024; v1 submitted 8 June, 2023; originally announced June 2023.

Journal ref: Phys. Rev. B 109, 155157 (2024)

Larmor precession in strongly correlated itinerant electron systems

Authors: Erik G. C. P. van Loon, Hugo U. R. Strand

Abstract: Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects… ▽ More Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials. △ Less

Submitted 16 October, 2023; v1 submitted 6 March, 2023; originally announced March 2023.

Journal ref: Commun Phys 6, 289 (2023)

Distinct spin and orbital dynamics in Sr$_{2}$RuO$_{4}$

Authors: H. Suzuki, L. Wang, J. Bertinshaw, H. U. R. Strand, S. Käser, M. Krautloher, Z. Yang, N. Wentzell, O. Parcollet, F. Jerzembeck, N. Kikugawa, A. P. Mackenzie, A. Georges, P. Hansmann, H. Gretarsson, B. Keimer

Abstract: The unconventional superconductor Sr$_2$RuO$_4$ has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru $L_3$-edge resonant inelastic x-ray scattering to obtain comprehensive maps of t… ▽ More The unconventional superconductor Sr$_2$RuO$_4$ has long served as a benchmark for theories of correlated-electron materials. The determination of the superconducting pairing mechanism requires detailed experimental information on collective bosonic excitations as potential mediators of Cooper pairing. We have used Ru $L_3$-edge resonant inelastic x-ray scattering to obtain comprehensive maps of the electronic excitations of Sr$_2$RuO$_4$ over the entire Brillouin zone. We observe multiple branches of dispersive spin and orbital excitations associated with distinctly different energy scales. The spin and orbital dynamical response functions calculated within the dynamical mean-field theory are in excellent agreement with the experimental data. Our results highlight the Hund metal nature of Sr$_{2}$RuO$_{4}$ and provide key information for the understanding of its unconventional superconductivity. △ Less

Submitted 30 November, 2022; originally announced December 2022.

Journal ref: Nat. Commun. 14, 7042 (2023)

Excitations and spectra from equilibrium real-time Green's functions

Authors: Xinyang Dong, Emanuel Gull, Hugo U. R. Strand

Abstract: The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the storage requirements of the discretized Green's function and the computational cost of solving the Dyson equation. In this manuscript, we apply a real-time discretiz… ▽ More The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the storage requirements of the discretized Green's function and the computational cost of solving the Dyson equation. In this manuscript, we apply a real-time discretization based on a piece-wise high-order orthogonal-polynomial expansion to address these issues. We present a superconvergent algorithm for solving the real-time equilibrium Dyson equation using the Legendre spectral method and the recursive algorithm for Legendre convolution. We show that the compact high order discretization in combination with our Dyson solver enables long-time simulations using far fewer discretization points than needed in conventional multistep methods. As a proof of concept, we compute the molecular spectral functions of H$_2$, LiH, He$_2$ and C$_6$H$_4$O$_2$ using self-consistent second-order perturbation theory and compare the results with standard quantum chemistry methods as well as the auxiliary second-order Green's function perturbation theory method. △ Less

Submitted 3 October, 2022; v1 submitted 8 June, 2022; originally announced June 2022.

Journal ref: Phys. Rev. B 106, 125153 (2022)

libdlr: Efficient imaginary time calculations using the discrete Lehmann representation

Authors: Jason Kaye, Kun Chen, Hugo U. R. Strand

Abstract: We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. The DLR basis consists of a collection of exponentials chosen by the interpolative decomposition to ensure stable and efficient recovery of Green's functions from imaginary time or Matsbuara frequency samples. The library provides subroutines to build the D… ▽ More We introduce libdlr, a library implementing the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. The DLR basis consists of a collection of exponentials chosen by the interpolative decomposition to ensure stable and efficient recovery of Green's functions from imaginary time or Matsbuara frequency samples. The library provides subroutines to build the DLR basis and grids, and to carry out various standard operations. The simplicity of the DLR makes it straightforward to incorporate into existing codes as a replacement for less efficient representations of imaginary time Green's functions, and libdlr is intended to facilitate this process. libdlr is written in Fortran, provides a C header interface, and contains a Python module pydlr. We also introduce a stand-alone Julia implementation, Lehmann.jl. △ Less

Submitted 21 June, 2022; v1 submitted 13 October, 2021; originally announced October 2021.

MSC Class: 81-04; 65D15 ACM Class: G.4; J.2; G.1.2

A fast time domain solver for the equilibrium Dyson equation

Authors: Jason Kaye, Hugo U. R. Strand

Abstract: We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solut… ▽ More We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled, nonlinear, convolutional Volterra integro-differential equations, for which the kernel depends self-consistently on the solution. As is typical in the numerical solution of Volterra-type equations, the computational bottleneck is the quadratic-scaling cost of history integration. However, the structure of the nonlinear Volterra integral operator precludes the use of standard fast algorithms. We propose a quasilinear-scaling FFT-based algorithm which respects the structure of the nonlinear integral operator. The resulting method can reach large propagation times, and is thus well-suited to explore quantum many-body phenomena at low energy scales. We demonstrate the solver with two standard model systems: the Bethe graph, and the Sachdev-Ye-Kitaev model. △ Less

Submitted 27 July, 2023; v1 submitted 12 October, 2021; originally announced October 2021.

MSC Class: 65R20; 81-08 ACM Class: G.1.9; G.1.0

Journal ref: Adv Comput Math 49, 63 (2023)

Inter-orbital singlet pairing in Sr$_2$RuO$_4$: a Hund's superconductor

Authors: Stefan Käser, Hugo U. R. Strand, Nils Wentzell, Antoine Georges, Olivier Parcollet, Philipp Hansmann

Abstract: We study the superconducting gap function of Sr$_2$RuO$_4$. By solving the linearized Eliashberg equation with a correlated pairing vertex extracted from a dynamical mean-field calculation we identify the dominant pairing channels. An analysis of the candidate gap functions in orbital and quasiparticle band basis reveals that an inter-orbital singlet pairing of even parity is in agreement with exp… ▽ More We study the superconducting gap function of Sr$_2$RuO$_4$. By solving the linearized Eliashberg equation with a correlated pairing vertex extracted from a dynamical mean-field calculation we identify the dominant pairing channels. An analysis of the candidate gap functions in orbital and quasiparticle band basis reveals that an inter-orbital singlet pairing of even parity is in agreement with experimental observations. It reconciles in particular the occurrence of a two-component order parameter with the presence of line-nodes of quasiparticles along the c-axis in the superconducting phase. The strong angular dependence of the gap along the Fermi surface is in stark contrast to its quasi-locality when expressed in the orbital basis. We identify local inter-orbital spin correlations as the driving force for the pairing and thus reveal the continuation of Hund's physics into the superconducting phase. △ Less

Submitted 18 May, 2021; originally announced May 2021.

Comments: 20 pages, 12 figures

Optical properties of LaNiO3 films tuned from compressive to tensile strain

Authors: I. Ardizzone, M. Zingl, J. Teyssier, H. U. R. Strand, O. Peil, J. Fowlie, A. B. Georgescu, S. Catalano, N. Bachar, A. B. Kuzmenko, M. Gibert, J. -M. Triscone, A. Georges, D. van der Marel

Abstract: Materials with strong electronic correlations host remarkable -- and technologically relevant -- phenomena such as magnetism, superconductivity and metal-insulator transitions. Harnessing and controlling these effects is a major challenge, on which key advances are being made through lattice and strain engineering in thin films and heterostructures, leveraging the complex interplay between electro… ▽ More Materials with strong electronic correlations host remarkable -- and technologically relevant -- phenomena such as magnetism, superconductivity and metal-insulator transitions. Harnessing and controlling these effects is a major challenge, on which key advances are being made through lattice and strain engineering in thin films and heterostructures, leveraging the complex interplay between electronic and structural degrees of freedom. Here we show that the electronic structure of LaNiO3 can be tuned by means of lattice engineering. We use different substrates to induce compressive and tensile biaxial epitaxial strain in LaNiO3 thin films. Our measurements reveal systematic changes of the optical spectrum as a function of strain and, notably, an increase of the low-frequency free carrier weight as tensile strain is applied. Using density functional theory (DFT) calculations, we show that this apparently counter-intuitive effect is due to a change of orientation of the oxygen octahedra.The calculations also reveal drastic changes of the electronic structure under strain, associated with a Fermi surface Lifshitz transition. We provide an online applet to explore these effects. The experimental value of integrated spectral weight below 2 eV is significantly (up to a factor of 3) smaller than the DFT results, indicating a transfer of spectral weight from the infrared to energies above 2 eV. The suppression of the free carrier weight and the transfer of spectral weight to high energies together indicate a correlation-induced band narrowing and free carrier mass enhancement due to electronic correlations. Our findings provide a promising avenue for the tuning and control of quantum materials employing lattice engineering. △ Less

Submitted 30 September, 2020; originally announced September 2020.

Comments: 12 pages, 11 figures

Journal ref: Phys. Rev. B 102, 155148 (2020)

Legendre-spectral Dyson equation solver with super-exponential convergence

Authors: Xinyang Dong, Dominika Zgid, Emanuel Gull, Hugo U. R. Strand

Abstract: Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving… ▽ More Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab inito problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution, enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He$_2$ within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of $10^{-9} E_h$ with only a few hundred expansion coefficients. △ Less

Submitted 5 April, 2020; v1 submitted 30 January, 2020; originally announced January 2020.

Journal ref: J. Chem. Phys. 152, 134107 (2020)

NESSi: The Non-Equilibrium Systems Simulation package

Authors: Michael Schüler, Denis Golež, Yuta Murakami, Nikolaj Bittner, Andreas Hermann, Hugo U. R. Strand, Philipp Werner, Martin Eckstein

Abstract: The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump-probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green's functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physical… ▽ More The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump-probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green's functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. We present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green's functions on the L-shaped Kadanoff-Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green's functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green's functions. The library employs a discretization of the Kadanoff-Baym contour into time $N$ points and a high-order implementation of integration routines. The total integrated error scales up to $\mathcal{O}(N^{-7})$, which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers. △ Less

Submitted 30 October, 2019; originally announced November 2019.

Comments: 86 pages, 15 figures

Strongly correlated materials from a numerical renormalization group perspective: How the Fermi-liquid state of Sr$_2$RuO$_4$ emerges

Authors: Fabian B. Kugler, Manuel Zingl, Hugo U. R. Strand, Seung-Sup B. Lee, Jan von Delft, Antoine Georges

Abstract: The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clea… ▽ More The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr$_2$RuO$_4$. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and Fermi-liquid behavior, concomitant with spin coherence, below a temperature of 25 K. By computing real-frequency correlation functions, we directly observe this spin--orbital scale separation and show that the van Hove singularity drives strong orbital differentiation. We extract quasiparticle interaction parameters from the low-energy spectrum and find an effective attraction in the spin-triplet sector. △ Less

Submitted 7 January, 2020; v1 submitted 5 September, 2019; originally announced September 2019.

Journal ref: Phys. Rev. Lett. 124, 016401 (2020)

Magnetic response of Sr$_2$RuO$_4$: quasi-local spin fluctuations due to Hund's coupling

Authors: Hugo U. R. Strand, Manuel Zingl, Nils Wentzell, Olivier Parcollet, Antoine Georges

Abstract: We study the magnetic susceptibility in the normal state of Sr$_2$RuO$_4$ using dynamical mean-field theory including dynamical vertex corrections. Besides the well known incommensurate response, our calculations yield quasi-local spin fluctuations which are broad in momentum and centered around the $Γ$ point, in agreement with recent inelastic neutron scattering experiments [P. Steffens, et al.,… ▽ More We study the magnetic susceptibility in the normal state of Sr$_2$RuO$_4$ using dynamical mean-field theory including dynamical vertex corrections. Besides the well known incommensurate response, our calculations yield quasi-local spin fluctuations which are broad in momentum and centered around the $Γ$ point, in agreement with recent inelastic neutron scattering experiments [P. Steffens, et al., Phys. Rev. Lett. 122, 047004 (2019)]. We show that these quasi-local fluctuations are controlled by the Hund's coupling and account for the dominant contribution to the momentum-integrated response. While all orbitals contribute equally to the incommensurate response, the enhanced $Γ$ point response originates from the planar xy orbital. △ Less

Submitted 15 April, 2019; originally announced April 2019.

Comments: 6 pages, 5 figures

Journal ref: Phys. Rev. B 100, 125120 (2019)

A comparative study of nonequilibrium insulator-to-metal transitions in electron-phonon systems

Authors: Sharareh Sayyad, Rok Zitko, Hugo U. R. Strand, Philipp Werner, Denis Golez

Abstract: We study equilibrium and nonequilibrium properties of electron-phonon systems described by the Hubbard-Holstein model using the dynamical mean-field theory. In equilibrium, we benchmark the results for impurity solvers based on the one-crossing approximation and slave-rotor approximation against non-perturbative numerical renormalization group reference data. We also examine how well the low energ… ▽ More We study equilibrium and nonequilibrium properties of electron-phonon systems described by the Hubbard-Holstein model using the dynamical mean-field theory. In equilibrium, we benchmark the results for impurity solvers based on the one-crossing approximation and slave-rotor approximation against non-perturbative numerical renormalization group reference data. We also examine how well the low energy properties of the electron-boson coupled systems can be reproduced by an effective static electron-electron interaction. The one-crossing and slave-rotor approximations are then used to simulate insulator-to-metal transitions induced by a sudden switch-on of the electron-phonon interaction. The slave-rotor results suggest the existence of a critical electron-phonon coupling above which the system is transiently trapped in a non-thermal metallic state with coherent quasiparticles. The same quench protocol in the one-crossing approximation results in a bad metallic state. △ Less

Submitted 3 October, 2018; originally announced October 2018.

Comments: 16 pages, 19 figures

Journal ref: Phys. Rev. B 99, 045118 (2019)

Theory of photoinduced ultrafast switching to a spin-orbital ordered `hidden' phase

Authors: Jiajun Li, Hugo U. R. Strand, Philipp Werner, Martin Eckstein

Abstract: Photoinduced hidden phases are often observed in materials with intertwined orders. Understanding the formation of these non-thermal phases is challenging and requires a resolution of the cooperative interplay between different orders on the ultrashort timescale. In this work, we demonstrate that non-equilibrium photo-excitations can induce a state with spin-orbital orders entirely different from… ▽ More Photoinduced hidden phases are often observed in materials with intertwined orders. Understanding the formation of these non-thermal phases is challenging and requires a resolution of the cooperative interplay between different orders on the ultrashort timescale. In this work, we demonstrate that non-equilibrium photo-excitations can induce a state with spin-orbital orders entirely different from the equilibrium state in the three-quarter-filled two-band Hubbard model. We identify a general mechanism governing the transition to the hidden state, which relies on a non-thermal partial melting of the intertwined orders mediated by photoinduced charge excitations in the presence of strong spin-orbital exchange interactions. Our study theoretically confirms the crucial role played by orbital degrees of freedom in the light-induced dynamics of strongly correlated materials and it shows that the switching to hidden states can be controlled already on the fs timescale of the electron dynamics. △ Less

Submitted 5 November, 2018; v1 submitted 5 June, 2018; originally announced June 2018.

Journal ref: Nature Commun. 9, 4581 (2018)

Coupled charge and spin dynamics in a photo-excited Mott insulator

Authors: Nikolaj Bittner, Denis Golež, Hugo U. R. Strand, Martin Eckstein, Philipp Werner

Abstract: Using a nonequilibrium implementation of the extended dynamical mean field theory (EDMFT) we simulate the relaxation after photo excitation in a strongly correlated electron system with antiferromagnetic spin interactions. We consider the $t$-$J$ model and focus on the interplay between the charge- and spin-dynamics in different excitation and doping regimes. The appearance of string states after… ▽ More Using a nonequilibrium implementation of the extended dynamical mean field theory (EDMFT) we simulate the relaxation after photo excitation in a strongly correlated electron system with antiferromagnetic spin interactions. We consider the $t$-$J$ model and focus on the interplay between the charge- and spin-dynamics in different excitation and doping regimes. The appearance of string states after a weak photo excitation manifests itself in a nontrivial scaling of the relaxation time with the exchange coupling and leads to a correlated oscillatory evolution of the kinetic energy and spin-spin correlation function. A strong excitation of the system, on the other hand, suppresses the spin correlations and results in a relaxation that is controlled by hole scattering. We discuss the possibility of detecting string states in optical and cold atom experiments. △ Less

Submitted 6 March, 2018; originally announced March 2018.

Journal ref: Phys. Rev. B 97, 235125 (2018)

Self-energy functional theory with symmetry breaking for disordered lattice bosons

Authors: Dario Hügel, Hugo U. R. Strand, Lode Pollet

Abstract: We extend the self-energy functional theory (SFT) to the case of interacting lattice bosons in the presence of symmetry breaking and quenched disorder. The self-energy functional we derive depends only on the self-energies of the disorder-averaged propagators, allowing for the construction of general non-perturbative approximations. Using a simple single-site reference system with only three varia… ▽ More We extend the self-energy functional theory (SFT) to the case of interacting lattice bosons in the presence of symmetry breaking and quenched disorder. The self-energy functional we derive depends only on the self-energies of the disorder-averaged propagators, allowing for the construction of general non-perturbative approximations. Using a simple single-site reference system with only three variational parameters, we are able to reproduce numerically exact quantum Monte Carlo (QMC) results on local observables of the Bose-Hubbard model with box disorder with high accuracy. At strong interactions, the phase boundaries are reproduced qualitatively but shifted with respect to the ones observed with QMC due to the extremely low condensate fraction in the superfluid phase. Deep in the strongly-disordered weakly-interacting regime, the simple reference system employed is insufficient and no stationary solutions can be found within its restricted variational subspace. By systematically analyzing thermodynamical observables and the spectral function, we find that the strongly-interacting Bose glass is characterized by different regimes, depending on which local occupations are activated as a function of the disorder strength. We find that the particles delocalize into isolated superfluid lakes over a strongly localized background around maximally-occupied sites whenever these sites are particularly rare. Our results indicate that the transition from the Bose glass to the superfluid phase around unit filling at strong interactions is driven by the percolation of superfluid lakes which form around doubly occupied sites. △ Less

Submitted 12 May, 2018; v1 submitted 22 January, 2018; originally announced January 2018.

Comments: 34 pages, 5 figures

Journal ref: Quantum Sci. Technol. 3 (2018) 034006

Hund's coupling driven photo-carrier relaxation in the two-band Mott insulator

Authors: Hugo U. R. Strand, Denis Golež, Martin Eckstein, Philipp Werner

Abstract: We study the relaxation dynamics of photo-carriers in the paramagnetic Mott insulating phase of the half-filled two-band Hubbard model. Using nonequilibrium dynamical mean field theory, we excite charge carriers across the Mott gap by a short hopping modulation, and simulate the evolution of the photo-doped population within the Hubbard bands. We observe an ultrafast charge-carrier relaxation driv… ▽ More We study the relaxation dynamics of photo-carriers in the paramagnetic Mott insulating phase of the half-filled two-band Hubbard model. Using nonequilibrium dynamical mean field theory, we excite charge carriers across the Mott gap by a short hopping modulation, and simulate the evolution of the photo-doped population within the Hubbard bands. We observe an ultrafast charge-carrier relaxation driven by emission of local spin excitations with an inverse relaxation time proportional to the Hund's coupling. The photo-doping generates additional side-bands in the spectral function, and for strong Hund's coupling, the photo-doped population also splits into several resonances. The dynamics of the local many-body states reveals two effects, thermal blocking and kinetic freezing, which manifest themselves when the Hund's coupling becomes of the order of the temperature or the bandwidth, respectively. These effects, which are absent in the single-band Hubbard model, should be relevant for the interpretation of experiments on correlated materials with multiple active orbitals. In particular, the features revealed in the non-equilibrium energy distribution of the photo-carriers are experimentally accessible, and provide information on the role of the Hund's coupling in these materials. △ Less

Submitted 20 April, 2017; originally announced April 2017.

Comments: 15 pages, 11 figures

Journal ref: Phys. Rev. B 96, 165104 (2017)

The anisotropic Harper-Hofstadter-Mott model: competition between condensation and magnetic fields

Authors: Dario Hügel, Hugo U. R. Strand, Philipp Werner, Lode Pollet

Abstract: We derive the reciprocal cluster mean-field method to study the strongly-interacting bosonic Harper-Hofstadter-Mott model. The system exhibits a rich phase diagram featuring band insulating, striped superfluid, and supersolid phases. Furthermore, for finite hopping anisotropy we observe gapless uncondensed liquid phases at integer fillings, which are analyzed by exact diagonalization. The liquid p… ▽ More We derive the reciprocal cluster mean-field method to study the strongly-interacting bosonic Harper-Hofstadter-Mott model. The system exhibits a rich phase diagram featuring band insulating, striped superfluid, and supersolid phases. Furthermore, for finite hopping anisotropy we observe gapless uncondensed liquid phases at integer fillings, which are analyzed by exact diagonalization. The liquid phases at fillings 1 and 3 exhibit the same band fillings as the fermionic integer quantum Hall effect, while the phase at filling 2 is CT-symmetric with zero charge response. We discuss how these phases become gapped on a quasi-one-dimensional cylinder, leading to a quantized Hall response, which we characterize by introducing a suitable measure for non-trivial many-body topological properties. Incompressible metastable states at fractional filling are also observed, indicating competing fractional quantum Hall phases. The combination of reciprocal cluster mean-field and exact diagonalization yields a promising method to analyze the properties of bosonic lattice systems with non-trivial unit cells in the thermodynamic limit. △ Less

Submitted 6 June, 2017; v1 submitted 13 September, 2016; originally announced September 2016.

Comments: 16 pages, 11 figures

Journal ref: Phys. Rev. B 96, 054431 (2017)

Bosonic self-energy functional theory

Authors: Dario Hügel, Philipp Werner, Lode Pollet, Hugo U. R. Strand

Abstract: We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies… ▽ More We derive the self-energy functional theory for bosonic lattice systems with broken $U(1)$ symmetry by parametrizing the bosonic Baym-Kadanoff effective action in terms of one- and two-point self-energies. The formalism goes beyond other approximate methods such as the pseudoparticle variational cluster approximation, the cluster composite boson mapping, and the Bogoliubov+U theory. It simplifies to bosonic dynamical-mean field theory when constraining to local fields, whereas when neglecting kinetic contributions of non-condensed bosons it reduces to the static mean-field approximation. To benchmark the theory we study the Bose-Hubbard model on the two- and three-dimensional cubic lattice, comparing with exact results from path integral quantum Monte Carlo. We also study the frustrated square lattice with next-nearest neighbor hopping, which is beyond the reach of Monte Carlo simulations. A reference system comprising a single bosonic state, corresponding to three variational parameters, is sufficient to quantitatively describe phase-boundaries, and thermodynamical observables, while qualitatively capturing the spectral functions, as well as the enhancement of kinetic fluctuations in the frustrated case. On the basis of these findings we propose self-energy functional theory as the omnibus framework for treating bosonic lattice models, in particular, in cases where path integral quantum Monte Carlo methods suffer from severe sign problems (e.g. in the presence of non-trivial gauge fields or frustration). Self-energy functional theory enables the construction of diagrammatically sound approximations that are quantitatively precise and controlled in the number of optimization parameters, but nevertheless remain computable by modest means. △ Less

Submitted 11 November, 2016; v1 submitted 4 March, 2016; originally announced March 2016.

Comments: 23 pages, 13 figures

Journal ref: Phys. Rev. B 94, 195119 (2016)

Beyond the Hubbard bands in strongly correlated lattice bosons

Authors: Hugo U. R. Strand, Martin Eckstein, Philipp Werner

Abstract: We investigate features in the single-particle spectral function beyond the Hubbard bands in the strongly correlated normal phase of the Bose-Hubbard model. There are two distinct classes of additional peaks generated by the bosonic statistics. The first type is thermally activated Hubbard "sidebands", with the same physical origin as the zero-temperature Hubbard bands, but generated by excitation… ▽ More We investigate features in the single-particle spectral function beyond the Hubbard bands in the strongly correlated normal phase of the Bose-Hubbard model. There are two distinct classes of additional peaks generated by the bosonic statistics. The first type is thermally activated Hubbard "sidebands", with the same physical origin as the zero-temperature Hubbard bands, but generated by excitations from thermally activated local occupation number states. The second class are two-particle fluctuation resonances driven by the lattice dynamics. In the unity filling Mott insulator, this takes the form of a localized triplon combined with a dispersing holon. Both types of resonances also manifest themselves in the structure factor and the interaction modulation spectra obtained from nonequilibrium bosonic dynamical mean-field theory calculations. Our findings explain experimental lattice modulation and Bragg spectroscopy results, and they predict a strong temperature dependence of the first sideband, thereby opening the door to precise thermometry of strongly correlated lattice bosons. △ Less

Submitted 9 December, 2015; v1 submitted 18 June, 2015; originally announced June 2015.

Comments: 9 pages, 3 figures, including appendices

Journal ref: Phys. Rev. A 92, 063602 (2015)

Nonequilibrium dynamical mean-field theory for bosonic lattice models

Authors: Hugo U. R. Strand, Martin Eckstein, Philipp Werner

Abstract: We develop the nonequilibrium extension of bosonic dynamical mean field theory (BDMFT) and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong coupling perturbative approaches, nonequilibrium BDMFT captures not only dynamical transitions, but also damping and thermalization effects at finite temperature. We apply the formalism to q… ▽ More We develop the nonequilibrium extension of bosonic dynamical mean field theory (BDMFT) and a Nambu real-time strong-coupling perturbative impurity solver. In contrast to Gutzwiller mean-field theory and strong coupling perturbative approaches, nonequilibrium BDMFT captures not only dynamical transitions, but also damping and thermalization effects at finite temperature. We apply the formalism to quenches in the Bose-Hubbard model, starting both from the normal and Bose-condensed phases. Depending on the parameter regime, one observes qualitatively different dynamical properties, such as rapid thermalization, trapping in metastable superfluid or normal states, as well as long-lived or strongly damped amplitude oscillations. We summarize our results in non-equilibrium "phase diagrams" which map out the different dynamical regimes. △ Less

Submitted 2 April, 2015; v1 submitted 27 May, 2014; originally announced May 2014.

Comments: 18 pages, 8 figures

Journal ref: Phys. Rev. X 5, 011038 (2015)

Principle of Maximum Entanglement Entropy and Local Physics of Correlated many-body Electron-Systems

Authors: Nicola Lanatà, Hugo U. R. Strand, Yongxin Yao, Gabriel Kotliar

Abstract: We argue that, because of the quantum-entanglement, the local physics of the strongly-correlated materials at zero temperature is described in very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits, and we perform numerical calculations of t… ▽ More We argue that, because of the quantum-entanglement, the local physics of the strongly-correlated materials at zero temperature is described in very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits, and we perform numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller Approximation (GA) that strongly support our theory in general. △ Less

Submitted 8 November, 2013; v1 submitted 28 October, 2013; originally announced October 2013.

Comments: Manuscript: 5 pages, 3 figures. Supplemental material: 1 page, 1 figure

Journal ref: Phys. Rev. Lett. 113, 036402 (2014)

Valence-skipping and negative-U in the d-band from repulsive local Coulomb interaction

Authors: Hugo U. R. Strand

Abstract: We show that repulsive local Coulomb interaction alone can drive valence-skipping charge disproportionation in the degenerate d-band, resulting in effective negative-U. This effect is shown to originate from anisotropic orbital-multipole scattering, and occurs only for $d^1$, $d^4$, $d^6$ and $d^9$ fillings (and their immediate surroundings). Explicit boundaries for valence-skipping are derived an… ▽ More We show that repulsive local Coulomb interaction alone can drive valence-skipping charge disproportionation in the degenerate d-band, resulting in effective negative-U. This effect is shown to originate from anisotropic orbital-multipole scattering, and occurs only for $d^1$, $d^4$, $d^6$ and $d^9$ fillings (and their immediate surroundings). Explicit boundaries for valence-skipping are derived and the paramagnetic phase diagram for $d^4$ and $d^6$ is calculated. We also establish that the valence-skipping metal is very different, in terms of its local valence distribution, compared to the atomic-like Hund's metal. These findings explains why transition metal compounds with the aforementioned d-band fillings are more prone to valence-skipping charge order and anomalous superconductivity. △ Less

Submitted 18 March, 2013; originally announced March 2013.

Comments: 5 pages, 5 figures

Journal ref: Phys. Rev. B 90, 155108 (2014)

Orbital Selectivity in Hund's metals: The Iron Chalcogenides

Authors: N. Lanatà, H. U. R. Strand, G. Giovannetti, B. Hellsing, L. de' Medici, M. Capone

Abstract: We show that electron correlations lead to a bad metallic state in chalcogenides FeSe and FeTe despite the intermediate value of the Hubbard repulsion $U$ and Hund's rule coupling $J$. The evolution of the quasi particle weight $Z$ as a function of the interaction terms reveals a clear crossover at $U \simeq$ 2.5 eV. In the weak coupling limit $Z$ decreases for all correlated $d$ orbitals as a fun… ▽ More We show that electron correlations lead to a bad metallic state in chalcogenides FeSe and FeTe despite the intermediate value of the Hubbard repulsion $U$ and Hund's rule coupling $J$. The evolution of the quasi particle weight $Z$ as a function of the interaction terms reveals a clear crossover at $U \simeq$ 2.5 eV. In the weak coupling limit $Z$ decreases for all correlated $d$ orbitals as a function of $U$ and beyond the crossover coupling they become weakly dependent on $U$ while strongly depend on $J$. A marked orbital dependence of the $Z$'s emerges even if in general the orbital-selective Mott transition only occurs for relatively large values of $U$. This two-stage reduction of the quasi particle coherence due to the combined effect of Hubbard $U$ and the Hund's $J$, suggests that the iron-based superconductors can be referred to as Hund's correlated metals. △ Less

Submitted 8 November, 2012; originally announced November 2012.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. B 87, 045122 (2013)

Distributional exact diagonalization formalism for quantum impurity models

Authors: Mats Granath, Hugo U. R. Strand

Abstract: We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Gree… ▽ More We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single impurity Anderson model and the two-orbital Hubbard model within dynamical mean field theory (DMFT) as well as real frequency data for self energy of the single band Hubbard model within DMFT using numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought. △ Less

Submitted 12 September, 2012; v1 submitted 30 January, 2012; originally announced January 2012.

Comments: Two band calculation updated, 4 pages, 4 figures

Journal ref: Phys. Rev. B 86, 115111 (2012)

Efficient implementation of the Gutzwiller variational method

Authors: Nicola Lanatà, Hugo U. R. Strand, Xi Dai, Bo Hellsing

Abstract: We present a self-consistent numerical approach to solve the Gutzwiller variational problem for general multi-band models with arbitrary on-site interaction. The proposed method generalizes and improves the procedure derived by Deng et al., Phys. Rev. B. 79 075114 (2009), overcoming the restriction to density-density interaction without increasing the complexity of the computational algorithm. Our… ▽ More We present a self-consistent numerical approach to solve the Gutzwiller variational problem for general multi-band models with arbitrary on-site interaction. The proposed method generalizes and improves the procedure derived by Deng et al., Phys. Rev. B. 79 075114 (2009), overcoming the restriction to density-density interaction without increasing the complexity of the computational algorithm. Our approach drastically reduces the problem of the high-dimensional Gutzwiller minimization by mapping it to a minimization only in the variational density matrix, in the spirit of the Levy and Lieb formulation of DFT. For fixed density the Gutzwiller renormalization matrix is determined as a fixpoint of a proper functional, whose evaluation only requires ground-state calculations of matrices defined in the Gutzwiller variational space. Furthermore, the proposed method is able to account for the symmetries of the variational function in a controlled way, reducing the number of variational parameters. After a detailed description of the method we present calculations for multi-band Hubbard models with full (rotationally invariant) Hund's rule on-site interaction. Our analysis shows that the numerical algorithm is very efficient, stable and easy to implement. For these reasons this method is particularly suitable for first principle studies -- e.g., in combination with DFT -- of many complex real materials, where the full intra-atomic interaction is important to obtain correct results. △ Less

Submitted 18 November, 2011; v1 submitted 31 July, 2011; originally announced August 2011.

Comments: 19 pages, 7 figures

Journal ref: Phys. Rev. B 85, 035133 (2012)

Discretized Thermal Green's Functions

Authors: Mats Granath, Andro Sabashvili, Hugo U. R. Strand, Stellan Östlund

Abstract: We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free energy. A conformal transformation is used to analytically continue the periodized Matsubara… ▽ More We present a spectral weight conserving formalism for Fermionic thermal Green's functions that are discretized in imaginary time and thus periodic in imaginary ("Matsubara") frequency. The formalism requires a generalization of the Dyson equation and the Baym-Kadanoff-Luttinger-Ward functional for the free energy. A conformal transformation is used to analytically continue the periodized Matsubara Green's function to the continuous real axis in a way that conserves the discontinuity at t=0 of the corresponding real-time Green's function. For given discretization the method allows numerical Green's function calculations of very high precision and it appears to give a well controlled convergent approximation as we decrease the discretization interval. The ideas are tested on Dynamical Mean Field Theory calculations of the paramagnetic Hubbard model. △ Less

Submitted 17 June, 2011; v1 submitted 17 March, 2011; originally announced March 2011.

Journal ref: Ann. Phys. 524, No. 3-4, 147-152 (2012)

Time-Dependent and Steady-State Gutzwiller approach for nonequilibrium transport in nanostructures

Authors: Nicola Lanatà, Hugo U. R. Strand

Abstract: We extend the time-dependent Gutzwiller variational approach, recently introduced by Schirò and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipa… ▽ More We extend the time-dependent Gutzwiller variational approach, recently introduced by Schirò and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipation in the leads, so that a steady state is reached after a sufficiently long relaxation time. The time-dependent method is applied to the single orbital Anderson impurity model at half-filling, modeling a quantum dot coupled to two leads. In these first exploratory calculations the Gutzwiller projector is limited to act only on the impurity. The strengths and the limitations of this approximation are assessed via comparison with state of the art continuous time quantum Monte Carlo results. Finally, we discuss how the method can be systematically improved by extending the region of action of the Gutzwiller projector. △ Less

Submitted 6 July, 2012; v1 submitted 14 February, 2011; originally announced February 2011.

Comments: 13 pages, 6 figures

Journal ref: Phys. Rev. B 86, 115310 (2012)

The Dynamical Mean Field Theory phase space extension and critical properties of the finite temperature Mott transition

Authors: Hugo U. R. Strand, Andro Sabashvili, Mats Granath, Bo Hellsing, Stellan Östlund

Abstract: We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical… ▽ More We consider the finite temperature metal-insulator transition in the half filled paramagnetic Hubbard model on the infinite dimensional Bethe lattice. A new method for calculating the Dynamical Mean Field Theory fixpoint surface in the phase diagram is presented and shown to be free from the convergence problems of standard forward recursion. The fixpoint equation is then analyzed using dynamical systems methods. On the fixpoint surface the eigenspectra of its Jacobian is used to characterize the hysteresis boundaries of the first order transition line and its second order critical end point. The critical point is shown to be a cusp catastrophe in the parameter space, opening a pitchfork bifurcation along the first order transition line, while the hysteresis boundaries are shown to be saddle-node bifurcations of two merging fixpoints. Using Landau theory the properties of the critical end point is determined and related to the critical eigenmode of the Jacobian. Our findings provide new insights into basic properties of this intensively studied transition. △ Less

Submitted 17 December, 2010; originally announced December 2010.

Comments: 11 pages, 12 figures, 1 table

Journal ref: Phys. Rev. B 83, 205136 (2011)