Imaginary-time quantum many-body theory out of equilibrium. II. Analytic continuation of dynamic observables and transport properties

Dirks, Andreas; Han, Jong E.; Jarrell, Mark; Pruschke, Thomas

doi:10.1103/physrevb.87.235140

Cited by 5 publications

(6 citation statements)

References 30 publications

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“…In the low-bias region, our results for the current-voltage characteristics agree with previous data (Heidrich-Meisner et al 14 ). We are able to extend earlier results 14,[36][37][38][39][40][41] to a wider parameter regime and discuss the interplay of finite lead bandwidth and electronic correlations. We find evidence for pronounced many-body effects at high-bias voltages in interplay with finite electronic bandwidths of the leads.…”

Section: Published By the American Physical Society Under The Terms Osupporting

confidence: 92%

Steady-state and quench-dependent relaxation of a quantum dot coupled to one-dimensional leads

et al. 2013

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We study the time evolution and steady state of the charge current in a single-impurity Anderson model, using matrix product states techniques. A nonequilibrium situation is imposed by applying a bias voltage across one-dimensional tight-binding leads. Focusing on particle-hole symmetry, we extract current-voltage characteristics from universal low-bias up to high-bias regimes, where band effects start to play a dominant role. We discuss three quenches, which after strongly quench-dependent transients yield the same steady-state current. Among these quenches we identify those favorable for extracting steady-state observables. The period of short-time oscillations is shown to compare well to real-time renormalization group results for a simpler model of spinless fermions. We find indications that many-body effects play an important role at high-bias voltage and finite bandwidth of the metallic leads. The growth of entanglement entropy after a certain time scale ∝ −1 is the major limiting factor for calculating the time evolution. We show that the magnitude of the steady-state current positively correlates with entanglement entropy. The role of high-energy states for the steady-state current is explored by considering a damping term in the time evolution.

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Section: Published By the American Physical Society Under The Terms Osupporting

confidence: 92%

Steady-state and quench-dependent relaxation of a quantum dot coupled to one-dimensional leads

et al. 2013

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“…In recent times a number of computational techniques have been devised to handle the SIAM out of equilibrium. Among them are scattering-state BA, 52 scattering-state NRG (SNRG), [53][54][55] non-crossing approximation studies, 56,57 fourth order Keldysh PT, 58 other perturbative methods 59,60 in combination with the renormalization group (RG), [61][62][63][64][65] iterative summation of real-time path integrals, 66 time dependent NRG, 67 flow equation techniques, 68,69 the time dependent density matrix RG (DMRG) [70][71][72][73][74][75] applied to the SIAM, 76,77 non-equilibrium cluster PT (CPT), 78 the non-equilibrium variational cluster approach (VCA), 79,80 dual fermions, 81 the func-tional RG (fRG), 82,83 diagrammatic QMC, 84,85 continuous time QMC (CT-QMC) calculations on an auxiliary system with an imaginary bias, [86][87][88][89][90] super operator techniques, 91,92 many-body PT and time-dependent density functional theory, 93 generalized slave-boson methods 94 , real-time RG (rtRG...…”

Section: Introductionmentioning

confidence: 99%

Auxiliary master equation approach to nonequilibrium correlated impurities

et al. 2014

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We present a numerical method for the study of correlated quantum impurity problems out of equilibrium, which is particularly suited to address steady state properties within Dynamical Mean Field Theory. The approach, recently introduced in [Arrigoni et al., Phys. Rev. Lett. 110, 086403 (2013)], is based upon a mapping of the original impurity problem onto an auxiliary open quantum system, consisting of the interacting impurity coupled to bath sites as well as to a Markovian environment. The dynamics of the auxiliary system is governed by a Lindblad master equation whose parameters are used to optimize the mapping. The accuracy of the results can be readily estimated and systematically improved by increasing the number of auxiliary bath sites, or by introducing a linear correction. Here, we focus on a detailed discussion of the proposed approach including technical remarks. To solve for the Green's functions of the auxiliary impurity problem, a non-hermitian Lanczos diagonalization is applied. As a benchmark, results for the steady state current-voltage characteristics of the single impurity Anderson model are presented. Furthermore, the bias dependence of the single particle spectral function and the splitting of the Kondo resonance are discussed. In its present form the method is fast, efficient and features a controlled accuracy. PACS numbers: 71.15.-m, 71.27+a, 73.63.Kv, 73.23.-b arXiv:1312.4586v2 [cond-mat.str-el]

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“…Among them are many-body cluster methods, 31,32 renormalization group (RG) approaches, [33][34][35][36][37][38][39] flow equation methods, 40,41 real-time path-integral calculations, 42 out-ofequilibrium noncrossing approximation (NCA), 94 generalized slave-boson methods, 12,96 diagrammatic quantum Monte Carlo (QMC), [43][44][45] or QMC methods based on a complex chemical potential. [46][47][48][49] The Gutzwiller approximation has been generalized to the time-dependent case 50 and so has numerical renormalization group (NRG) [51][52][53][54] where however some issues with the use of Wilson chains in nonequilibrium systems have been pointed out by Rosch. 55 Dual-fermion approaches 56 have been proposed as well as superoperator techniques. 57,58 Some recent work attempts to compare several of these theories [59][60][61] and shed light on the critical issue of time scales involved.…”

Section: Published By the American Physical Society Under The Terms Omentioning

confidence: 99%

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

et al. 2012

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We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of nonequilibrium cluster perturbation theory and the nonequilibrium variational cluster approach, respectively. Results for the steady-state current are benchmarked against data from accurate matrix product state based time evolution. We show that for low to medium interaction strength, nonequilibrium cluster perturbation theory already yields good results, while for higher interaction strength the self-consistent feedback of the nonequilibrium variational cluster approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the nonequilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle-hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [A. V. Kretinin et al., Phys. Rev. B 84, 245316 (2011)].

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Imaginary-time quantum many-body theory out of equilibrium. II. Analytic continuation of dynamic observables and transport properties

Cited by 5 publications

References 30 publications

Steady-state and quench-dependent relaxation of a quantum dot coupled to one-dimensional leads

Steady-state and quench-dependent relaxation of a quantum dot coupled to one-dimensional leads

Auxiliary master equation approach to nonequilibrium correlated impurities

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

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