# The Anderson impurity model out of equilibrium: Assessing the accuracy of simulation techniques with an exact current-occupation relation

## TL;DR

This paper establishes an exact current-occupation relation in the nonequilibrium Anderson impurity model and uses it to evaluate the accuracy of various simulation techniques, revealing discrepancies and solutions.

## Contribution

It introduces an exact steady-state current-occupation relation for the Anderson model and demonstrates its use in assessing the accuracy of different simulation methods.

## Key findings

- Standard calculations violate the current-occupation relation in the Anderson-Holstein model.
- Numerical procedures can resolve the violations efficiently.
- The relation is satisfied in the Anderson model with electron-electron interactions using a deterministic scheme.

## Abstract

We study the interacting, symmetrically coupled single impurity Anderson model. By employing the nonequilibrium Green's function formalism, we establish an exact relationship between the steady-state charge current flowing through the impurity (dot) and its occupation. We argue that the steady state current-occupation relation can be used to assess the consistency of simulation techniques, and identify spurious transport phenomena. We test this relation in two different model variants: First, we study the Anderson-Holstein model in the strong electron-vibration coupling limit using the polaronic quantum master equation method. We find that the current-occupation relation is violated numerically in standard calculations, with simulations bringing up incorrect transport effects. Using a numerical procedure, we resolve the problem efficiently. Second, we simulate the Anderson model with electron-electron interaction on the dot using a deterministic numerically-exact time-evolution scheme. Here, we observe that the current-occupation relation is satisfied in the steady-state limit---even before results converge to the exact limit.