Steady-state and quench dependent relaxation of a quantum dot coupled to one-dimensional leads

TL;DR

This paper investigates the charge current dynamics and steady states in a quantum dot coupled to one-dimensional leads using matrix product states, revealing the effects of quenches, bias voltage, and many-body interactions.

Contribution

It introduces a detailed analysis of steady-state current formation in a quantum dot system under nonequilibrium conditions, highlighting quench protocols and many-body effects.

Findings

Steady-state current is independent of quench type after transient effects.

Short-time oscillation periods match real-time renormalization group predictions.

High-bias voltage and finite bandwidth enhance many-body effects.

Abstract

We study the time evolution and steady state of the charge current in a single-impurity Anderson model, using matrix product states techniques. A nonequilibrium situation is imposed by applying a bias voltage across one-dimensional tight-binding leads. Focusing on particle-hole symmetry, we extract current-voltage characteristics from universal low-bias up to high-bias regimes, where band effects start to play a dominant role. We discuss three quenches, which after strongly quench-dependent transients yield the same steady-state current. Among these quenches we identify those favorable for extracting steady-state observables. The period of short-time oscillations is shown to compare well to real-time renormalization group results for a simpler model of spinless fermions. We find indications that many-body effects play an important role at high-bias voltage and finite bandwidth of the metallic leads. The growth of entanglement entropy after a certain time scale (proportional to the inverse of Delta) is the major limiting factor for calculating the time evolution. We show that the magnitude of the steady-state current positively correlates with entanglement entropy. The role of high-energy states for the steady-state current is explored by considering a damping term in the time evolution.