Impurity model for non-equilibrium steady states

We examine how non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the non-analytic potential arises from the different density of states of the baths. In periodically driven-dissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The mean-field critical exponents become dependent on the low-energy features of the two most singular baths. We propose an extension beyond mean field.

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“…3.2 led us to the same definition for the effective meanfield potential V NESS (ϕ) in Eqs. (13) and (18). We argue in App.…”

Section: Finite-size Fully-connected Modelmentioning

confidence: 84%

“…Effective potential Using the definition in Eqs. (13) or (18) with D(ϕ) := 1, we obtain the following effective potential…”

Section: Mean-field Lindblad Descriptionmentioning

confidence: 99%

Landau theory for non-equilibrium steady states

Aron

Chamon

2020

SciPost Phys.

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“…Furthermore, for its simplicity the fermion bath model can be used as an ideal building block for studying strong correlation effects in lattice driven out of equilibrium. Particularly, with the time-independent Coulomb gauge DMFT can be readily formulated using the scattering state method [12][13][14]23 It is well-known in equilibrium strong correlation physics that electrons undergo collective state when a strong interaction is present, with some emergent energy scale T * . One may speculate that an electric field of order Ω ∼ T * would significantly alter the strongly correlated state.…”

Section: Discussionmentioning

confidence: 99%

“…There have been numerous attempts to simulate nonequilibrium physics in lattice models, often through isolated Hamiltonians 15,[17][18][19] suited for quench dynamics of cold atom systems in optical lattice, periodically driven systems 19,20 , and some basic dissipation models 19,[21][22][23][24] .…”

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confidence: 99%

Energy dissipation in a dc-field-driven electron lattice coupled to fermion baths

Han

2013

Phys. Rev. B

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Electron transport in electric-field-driven tight-binding lattice coupled to fermion baths is comprehensively studied. We reformulate the problem by using the scattering state method within the Coulomb gauge. Calculations show that the formulation justifies direct access to the steady-state bypassing the time-transient calculations, which then makes the steady-state methods developed for quantum dot theories applicable to lattice models. We show that the effective temperature of the hot-electron induced by a DC electric field behaves as T eff = Cγ(Ω/Γ) with a numerical constant C, tight-binding parameter γ, the Bloch oscillation frequency Ω and the damping parameter Γ. In the small damping limit Γ/Ω → 0, the steady-state has a singular property with the electron becoming extremely hot in an analogy to the short-circuit effect. This leads to the conclusion that the dissipation mechanism cannot be considered as an implicit process, as treated in equilibrium theories. Finally, using the energy flux relation, we derive a steady-state current for interacting models where only on-site Green's functions are necessary.

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“…Another intriguing application occurs in dynamical mean field theory [2,[4][5][6], where lattice problems either in or out of equilibrium are mapped to impurity problems with an environment that is determined by a self-consistency criterion. This has been important, for instance, in understanding the metal-insulator transition in materials like transition metal oxides [4,6,7] and has become an important paradigm in studying nonequilibrium effects in extended interacting systems, including thermalization after an interaction quench [8,9], the nonequilibrium steady state [10,11] and Bloch oscillations [5,12,13] under the influence of a static electric field. Thus, the theoretical description of impurity problems is a key element in understanding a wide range of phenomena, in particular nonequilibrium effects.…”

Section: Introductionmentioning

confidence: 99%

Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

et al. 2015

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We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort.We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the non-monotonic temperature dependence of the steadystate magnetization as a result of competing broadening effects. We also elucidate the pronounced non-linear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.

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Impurity model for non-equilibrium steady states

Cited by 12 publications

References 21 publications

Landau theory for non-equilibrium steady states

Landau theory for non-equilibrium steady states

Energy dissipation in a dc-field-driven electron lattice coupled to fermion baths

Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

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