A Numerical Renormalization Group approach to Non-Equilibrium Green's Functions for Quantum Impurity Models

TL;DR

This paper introduces a numerical renormalization group method for calculating non-equilibrium Green's functions in quantum impurity models, enabling accurate steady-state spectral analysis under various conditions.

Contribution

It extends NRG techniques to non-equilibrium scenarios, ensuring spectral sum-rule conservation and providing a practical approach for steady-state spectral functions.

Findings

Excellent agreement with equilibrium spectra for finite U

Method accurately captures steady-state spectral functions

Applicable to nano-device bias conditions

Abstract

We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfills the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion $U>0$ is switched on at $t=0$, and the asymptotic steady-state spectral functions are obtained for various values of $U$ as well as magnetic field strength $H$ and temperature $T$. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite $U$. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nano-devices.