Nonperturbative Green's function technique for nonequilibrium steady state

TL;DR

This paper introduces a nonperturbative Green's function method in resolvent form for analyzing steady-state transport in quantum impurity systems, advancing understanding of phenomena like the Kondo effect.

Contribution

It develops a systematic basis vector collection method in Liouville space for resolvent Green's functions, applicable to single-impurity Anderson models with multiple reservoirs.

Findings

Derived all basis vectors for single-impurity Anderson models

Applied method to study Kondo phenomenon under bias

Enhanced nonperturbative analysis of steady-state transport

Abstract

Nonperturbative dynamic theory has a particular advantage in studying the transport in a quantum impurity system in a steady state. Here, we develop a new approach for obtaining the retarded Green's function expressed in resolvent form. We use the Heisenberg picture to facilitate dynamic theory and propose a new systematic method of collecting the basis vectors spanning the Liouville space, which is the most crucial step in obtaining the resolvent Green's function. We obtain all the linearly independent basis vectors for studying the single-impurity Anderson models with one and two reservoirs. The latter is an appropriate model for studying the Kondo phenomenon in a steady state when a bias is applied. This is one of long standing subjects in theoretical condensed matter physics.