Auxiliary Master Equation for Nonequilibrium Dual-Fermion Approach

Abstract

We introduce auxiliary quantum master equation -dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference much closer to the true nonequilibrium state than in the original dual fermion formulation. In steady-state situations, the scheme is numerically cheaper and allows to avoid long time propagation of previous considerations. Anderson impurity is used as a test model. The QME-DF simulations are compared with numerically exact tdDMRG results.

Markovian treatment of non-Markovian dynamics of open Fermionic systems

“…We note in passing that the dual fermion approach relies on ability to evaluate multi-time correlation function in the aux system representing phys dynamics. Thus, proof of equivalence of multi-time correlation functions in phys and aux systems presented above is important for building theoretical foundation for the aux-DF method of [19].…”

“…Alternative (or complementary) strategy is utilization of small number of auxiliary modes (thus, relying on relatively poor fitting) with implementation of a procedure accounting for the difference between hybridization functions of the phys and aux systems. Such approach was implemented in [19] within the dual fermion technique. The technique employs an auxiliary fermionic degree of freedom-dual fermion-which provides a way to account for the difference in the form of diagrammatic expansion.…”

“…This allows to get accurate results employing smaller number of auxiliary modes. However, additional procedure (superperturbation theory) is required on top of the QME solution (see [19] and references therein for technical details). We note in passing that the dual fermion approach relies on ability to evaluate multi-time correlation function in the aux system representing phys dynamics.…”

“…We note that the example is a simple illustration only and that realistic simulations will require more than two auxiliary modes and/or procedure to correct for approximate hybridization function to reproduce dynamics in the physical system. Such considerations have been done by us previously [19,24].…”

“…Within AMEA the original unitary evolution is substituted with a Lindblad-type quantum master equation consideration of an expanded system (system plus set of auxiliary modes). Another example is the recent formulation of the auxiliary dual-fermion (aux-DF) method [19]. Aux-DF technique complements the mapping with a procedure correcting for deviation of original hybridization functions from those in the auxiliary system.…”