Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach

TL;DR

This paper introduces a time-dependent numerical renormalization group method to study the nonequilibrium dynamics of quantum impurity systems, accurately capturing their real-time evolution and relaxation behaviors.

Contribution

It presents a novel approach combining NRG with a complete basis set for arbitrary coupling strengths, enabling detailed analysis of quantum impurity dynamics out of equilibrium.

Findings

Benchmark against exact solutions confirms accuracy.

Identifies distinct relaxation times for spin and charge.

Demonstrates method's effectiveness in quantum dot dynamics.

Abstract

We develop a general approach to the nonequilibrium dynamics of quantum impurity systems for arbitrary coupling strength. The numerical renormalization group is used to generate a complete basis set necessary for the correct description of the time evolution. We benchmark our method with the exact analytical solution for the resonant-level model. As a first application, we investigate the equilibration of a quantum dot subject to a sudden change of the gate voltage and external magnetic field. Two distinct relaxation times are identified for the spin and charge dynamics.