Approach to a stationary state in a driven Hubbard model coupled to a thermostat

Amaricci, A.; Weber, Cédric; Capone, Massimo; Kotliar, Gabriel

doi:10.1103/physrevb.86.085110

Cited by 69 publications

(86 citation statements)

References 26 publications

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“…The weak-coupling perturbation theory has been used for a long time as an impurity solver in equilibrium DMFT calculations (Georges and Kotliar, 1992;Zhang, Rozenberg, and Kotliar, 1993;Freericks, 1994;Freericks and Jarrell, 1994;Georges et al, 1996), and in the nonequilibrium DMFT context, it has enabled a range of studies of the Hubbard model (Schmidt and Monien, 2002;Heary and Han, 2009;Eckstein and Werner, 2011a;Amaricci et al, 2012;Aron, Kotliar, and Weber, 2012;Tsuji et al, 2012;Tsuji, Eckstein, and Werner, 2013) and of the FalicovKimball model (Turkowski and Freericks, 2007a).…”

Section: Weak-coupling Perturbation Theorymentioning

confidence: 99%

“…While bare second-order perturbation theory fails for the quench to U ¼ 5, it at least reproduces the short-time dynamics correctly. For driven steady states (Amaricci et al, 2012), the accuracy of the weak-coupling approach has yet to be tested in detail. Here the nonconserving nature of the approximation becomes apparent when the energy current to the reservoir differs from the power injected by the field [Eq.…”

Section: Weak-coupling Perturbation Theorymentioning

confidence: 99%

“…Two dissipation mechanisms have so far been considered within DMFT: (i) the free-fermion bath (Büttiker model, Sec. II.A.2.b), in which one additional reservoir of particles is coupled to each lattice site (Tsuji, Oka, and Aoki, 2009;Amaricci et al, 2012;Aron, 2012;, and (ii) the coupling to a bath of harmonic oscillator modes Werner, 2013a, 2013c;Kemper et al, 2013). For the Büttiker model, the systembath coupling is bilinear in the fermion creation and annihilation operators, such that additional degrees of freedom can be integrated out exactly.…”

Section: Dissipative Systemsmentioning

confidence: 99%

“…(55). In spite of its apparent simplicity and the absence of momentum scattering, the model can lead to a physically meaningful steady state (Amaricci et al, 2012;. For the bosonic bath, one considers an infinite set of phonons, coupled via the Holstein coupling (81).…”

Section: Dissipative Systemsmentioning

confidence: 99%

“…When the system is excited by an external field, the energy injected from the field flows to the bath, resulting in the energy dissipation. The simplest model of the heat bath, that can be solved analytically, is a free-fermion bath (Tsuji, Oka, and Aoki, 2009;Amaricci et al, 2012;Aron, 2012; defined by…”

Section: B Free-fermion Bathmentioning

confidence: 99%

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Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

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The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a selfconsistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

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Section: Weak-coupling Perturbation Theorymentioning

confidence: 99%

Section: Weak-coupling Perturbation Theorymentioning

confidence: 99%

Section: Dissipative Systemsmentioning

confidence: 99%

Section: Dissipative Systemsmentioning

confidence: 99%

Section: B Free-fermion Bathmentioning

confidence: 99%

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Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

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Iterated Perturbation Theory for Mott Insulators in a Static Electric Field with Optical Phonons

Mazzocchi,

Arrigoni

2024

Physica Status Solidi (b)

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This article aims to compare the so‐called iterated perturbation theory (IPT) and auxiliary master equation approach (AMEA) impurity solvers for a Mott insulating system driven out of equilibrium by a static electric field. Electronic heat bath and optical phonons are employed as dissipation mechanism of the current‐induced Joule heat that the excited electrons of the lattice experience as the result of the field's driving. Despite its simplicity, the IPT approach yields results that qualitatively are in good agreement with those obtained within the AMEA impurity solver, although fails to reproduce some correlation effects.

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Nonequilibrium DMFT

Turkowski

2021

Dynamical Mean-Field Theory for Strongly Correlated Materials

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Approach to a stationary state in a driven Hubbard model coupled to a thermostat

Cited by 69 publications

References 26 publications

Nonequilibrium dynamical mean-field theory and its applications

Nonequilibrium dynamical mean-field theory and its applications

Iterated Perturbation Theory for Mott Insulators in a Static Electric Field with Optical Phonons

Nonequilibrium DMFT

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