Many-body wavefunctions for quantum impurities out of equilibrium. II. Charge fluctuations

TL;DR

This paper develops a formalism to analyze charge fluctuations in quantum impurity models out of equilibrium, providing exact wavefunctions and steady state properties for the resonant level and Anderson models.

Contribution

It extends previous work to include charge fluctuation models, deriving exact wavefunctions and steady states, and validating results with perturbation theory.

Findings

Exact time-evolving wavefunction for the resonant level model.

Steady state impurity occupancy calculated to leading order in interaction.

Steady state current in the Anderson model matches Keldysh perturbation theory.

Abstract

We extend the general formalism discussed in the previous paper [A. B. Culver and N. Andrei, Phys. Rev. B 103, 195106 (2021)] to two models with charge fluctuations: the interacting resonant level model and the Anderson impurity model. In the interacting resonant level model, we find the exact time-evolving wavefunction and calculate the steady state impurity occupancy to leading order in the interaction. In the Anderson impurity model, we find the nonequilibrium steady state for small or large Coulomb repulsion $U$, and we find that the steady state current to leading order in $U$ agrees with a Keldysh perturbation theory calculation.