Periodically refreshed baths to simulate open quantum many-body dynamics

TL;DR

This paper introduces a recursive formalism to accurately simulate the full non-Markovian dynamics of open quantum many-body systems connected to finite baths, enabling analysis of complex non-equilibrium steady states.

Contribution

The authors develop a general recursive method to reconstruct exact non-Markovian dynamics of open quantum systems with finite baths, surpassing current limitations.

Findings

Successfully simulated non-Markovian dynamics of interacting fermionic chains.

Reconstructed dynamics without small parameter approximations.

Analyzed systems with finite temperature and voltage biases.

Abstract

Obtaining dynamics of an interacting quantum many-body system connected to multiple baths initially at different, finite, temperatures and chemical potentials is a challenging problem. This is due to a combination of the prevalence of strong correlations in the system, the infinite nature of the baths and the long time to reach steady state. In this work we develop a general formalism that allows access to the full non-Markovian dynamics of such open quantum many-body systems up to the non-equilibrium steady state (NESS), provided its uniqueness. Specifically, we show how finite-time evolution in presence of finite-sized baths, whose opportune size is determined by their original spectral density, can be recursively used to faithfully reconstruct the exact dynamics without requiring any small parameter. Such a reconstruction is possible even in parameter regimes which would otherwise be inaccessible by current state-of-the-art techniques. We specifically demonstrate this by obtaining the full numerically exact non-Markovian dynamics of interacting fermionic chains in two terminal set-ups with finite temperature and voltage biases, a problem which previously remained outstanding despite its relevance in a wide range of contexts, for example, quantum heat engines and refrigerators.