Flow Equation Calculation of Transient and Steady State Currents in the Anderson Impurity Model

TL;DR

This paper introduces a new analytical flow equation method to calculate transient and steady state currents in the Anderson impurity model, capturing the real-time buildup of current after sudden coupling activation.

Contribution

The paper presents a novel flow equation approach for analyzing non-equilibrium currents in the Anderson impurity model beyond linear response.

Findings

Successfully models the real-time buildup of current.

Provides analytical expressions for steady state currents.

Applicable to the mixed valence regime.

Abstract

Transient and steady state currents through dc-biased quantum impurity models beyond the linear response regime are of considerable interest, both from an experimental and a theoretical point of view. Here we present a new analytical approach for the calculation of such currents based on the flow equation method (method of infinitesimal unitary transformations). Specifically, we analyze the Anderson impurity model in its mixed valence regime where the coupling to the leads is switched on suddenly at time $t=0$. We observe the real time buildup of the current until it reaches its steady state limit.