Tensor-network approach to thermalization in open quantum many-body systems

TL;DR

This paper uses tensor-network methods to study how open quantum many-body systems relax to thermal equilibrium, showing that under certain conditions, the system's state remains thermal with a changing temperature.

Contribution

It introduces a tensor-network approach for simulating the dynamics of open quantum systems and a method to compare states for thermodynamic equivalence.

Findings

Time-evolved states are indistinguishable from Gibbs states with a time-dependent temperature.

The method works in the thermodynamic limit for weak dissipation.

The approach provides insights into thermalization processes in open quantum systems.

Abstract

We investigate the relaxation dynamics of open non-integrable quantum many-body systems in the thermodynamic limit by using a tensor-network formalism. We simulate the Lindblad quantum master equation (LQME) of infinite systems by making use of the uniform matrix product operators (MPO) as the ansatz of their density matrices. Furthermore, we establish a method to measure the thermodynamic equivalence between two states described by the uniform MPOs. We numerically show that when an initial state of the LQME is a thermal Gibbs state, a time evolved state is always indistinguishable from a Gibbs state with a time-dependent effective temperature in the weak-dissipation and thermodynamic limit.