# Auxiliary master equation approach within stochastic wave functions: Application to the Interacting Resonant Level Model

## TL;DR

This paper advances the auxiliary master equation approach (AMEA) by integrating stochastic wave functions, enabling faster and more accurate simulations of the Interacting Resonant Level Model in and out of equilibrium.

## Contribution

The paper introduces a stochastic wave functions implementation within AMEA, significantly reducing computation time and improving accuracy for many-body quantum system simulations.

## Key findings

- Enhanced simulation speed with stochastic wave functions
- Accurate current-voltage and correlation function results
- Effective extrapolation to infinite auxiliary bath sites

## Abstract

We present further developments of the auxiliary master equation approach (AMEA), a numerical method to simulate many-body quantum systems in as well as out of equilibrium, and apply it to the Interacting Resonant Level Model (IRLM) to benchmark the new developments. In particular, our results are obtained by employing the stochastic wave functions (SWF) method to solve the auxiliary open quantum system arising within AMEA. This development allows to reach extremely low wall-times for the calculation of correlation functions with respect to previous implementations of AMEA. An additional significant improvement is obtained by extrapolating a series of results obtained by increasing the number of auxiliary bath sites, $N_B$, used within the auxiliary open quantum system formally to the limit of $ N_B \rightarrow \infty$. Results for the current-voltage characteristics and for equilibrium correlation functions are compared with the one obtained by exact and matrix-product based approaches.