Imaginary-time quantum many-body theory out of equilibrium: Formal equivalence to Keldysh real-time theory and calculation of static properties

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

doi:10.1103/physrevb.86.155130

Cited by 17 publications

(30 citation statements)

References 66 publications

(53 reference statements)

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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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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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“…Unfortunately, the non-locality of the current operator and the rather complicated analytical structure of the local Green's functions render such calculations very difficult [28]. However, obtaining results for static local quantities, such as the double occupancy on the dot or the magnetization, is relatively straightforward [27].…”

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confidence: 99%

“…The main challenge in this approach is to map the auxiliary systems back onto the real one, which can be accomplished by a standard maximum entropy analytical continuation procedure [26]. Details of the numerical procedure have been provided in a recent publication [27]. Here, we compare the results of this Matsubara-voltage quantum Monte Carlo (MV-QMC) approach to data obtained with a scatteringstates numerical renormalization group (SNRG) method [19,29,30] and real-time quantum Monte Carlo (RT-QMC) [17,18].…”

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confidence: 99%

Double occupancy and magnetic susceptibility of the Anderson impurity model out of equilibrium

Dirks

Schmitt

Han

et al. 2013

EPL

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-We use different numerical approaches to calculate the double occupancy and magnetic susceptibility as a function of a bias voltage in an Anderson impurity model. Specifically, we compare results from the Matsubara-voltage quantum Monte-Carlo approach (MV-QMC), the scattering-states numerical renormalization group (SNRG), and real-time quantum Monte-Carlo (RT-QMC), covering Coulomb repulsions ranging from the weak-coupling well into the strongcoupling regime. We observe a distinctly different behavior of the double occupancy and the magnetic response. The former measures charge fluctuations and thus only indirectly exhibits the Kondo scale, while the latter exhibits structures on the scale of the equilibrium Kondo temperature. The Matsubara-voltage approach and the scattering-states numerical renormalization group yield consistent values for the magnetic susceptibility in the Kondo limit. On the other hand, all three numerical methods produce different results for the behavior of charge fluctuations in strongly interacting dots out of equilibrium.

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“…The charge and energy currents can be calculated from the NE average expression in Equation (4) [34], from asymptotic steady state scattering techniques [12,[53][54][55][56][57] or from an NE Green's function (NEGF) approach [11,13]. The full equivalence between the asymptotic steady state scattering and the NEGF techniques has been shown in [58].…”

Section: An Examplementioning

confidence: 99%

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

Ness

2017

Entropy

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Abstract:We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs-von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.

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Imaginary-time quantum many-body theory out of equilibrium: Formal equivalence to Keldysh real-time theory and calculation of static properties

Cited by 17 publications

References 66 publications

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

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

Double occupancy and magnetic susceptibility of the Anderson impurity model out of equilibrium

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

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