# Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath

## TL;DR

This paper derives a Lindblad master equation for a Lipkin-Meshkov-Glick model coupled to a bosonic bath, demonstrating how the bath induces thermalization in the system and analyzing the thermalization rate for large systems.

## Contribution

The work explicitly proves that a bosonic bath induces thermalization in the LMG model, which is otherwise non-thermalizing due to integrability.

## Key findings

- Operators reach thermal equilibrium values at long times
- Thermalization rate is calculated for large system sizes
- Bath coupling restores thermalization in the LMG model

## Abstract

We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalization on this otherwise non-thermalizing model outlines an avenue towards probing the unconventional thermodynamic properties predicted to occur in ultracold-atom-based realizations of the LMG model.