CT-QMC and Maximum Entropy Approach to a Scattering-States Formulation of Strongly Correlated Steady-State Transport

Abstract

Abstract. In a recent work [17] Han and Heary introduced a formalism approaching steadystate quantum transport through mesoscopic structures which maps the non-equilibrium problem onto a family of auxiliary equilibrium quantum impurity systems by introducing imaginary voltages. We apply continuous-time quantum Monte-Carlo solvers to obtain precise and unbiased imaginary-time data for these auxiliary models. Physical observables are obtained by an analytical continuation in both Matsubara frequency and complexified voltage using a Maximum Entropy Method (MEM). The MEM is introduced by means of a kernel function compatible with the analytical structure of the theory. While it remains a yet challenging task to obtain reliable spectral functions, this unbiased procedure seems to indicate that the formalism yields results which are compatible with those of other methods. IntroductionCalculating steady-state transport properties of open quantum systems is a challenging and unsolved problem. It has been approached by perturbative methods [1][2][3], the time-dependent density matrix renormalization group (t-DMRG) [4,5], real-time quantum Monte Carlo (RT-QMC) [6][7][8][9], numerical renormalization group (NRG) [10], and the functional renormalization group (fRG) [11][12][13][14][15][16]. However, none of the methods developed so far is able to give a complete and reliable description of the physical properties in all parameter regimes. More importantly, the most interesting regime, where all relevant energy scales -voltage, temperature, magnetic field, etc. -are of the same order as the low-energy scale of the Anderson Impurity Model, is usually not accessible. Therefore, the development of new or improved simulation approaches is a worthwhile and important task.Recently, a new and rather unconventional approach to calculate the steady-state transport through interacting quantum dots or similar structures was proposed by Han and Heary [17]. Their formalism, which is based on Hershfield's density operator [18], maps the non-equilibrium steady-state of the interacting model onto an infinite set of auxiliary equilibrium systems, each characterized by some complex voltage. The complexification of the voltage bias, however, introduces a formidable new problem in the form of an analytical continuation with respect to

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

“…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.…”

“…Recently moreover, several techniques, which have proven very successful in the equilibrium theory, have been extended to the non-equilibrium case. 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 of equilibrium 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 non-equilibrium systems have been pointed out by Rosch 55 .…”