Thermalization of the Lipkin-Meshkov-Glick model in blackbody radiation

TL;DR

This paper investigates how the Lipkin-Meshkov-Glick model thermalizes under blackbody radiation, revealing conditions for complete or partial thermalization and analyzing how thermalization time scales with system size, especially near critical points.

Contribution

It applies Lindblad-based equations to the LMG model in blackbody radiation, providing analytical insights into thermalization regimes and time scaling near critical points.

Findings

Complete thermalization occurs at high density.

Partial thermalization within fixed total spin subspaces at low density.

Thermalization time diverges with system size at critical points.

Abstract

In a recent work, we have derived simple Lindblad-based equations for the thermalization of systems in contact with a thermal reservoir. Here, we apply these equations to the Lipkin-Meshkov-Glick model (LMG) in contact with a blackbody radiation and analyze the dipole matrix elements involved in the thermalization process. We find that the thermalization can be complete only if the density is sufficiently high, while, in the limit of low density, the system thermalizes partially, namely, within the Hilbert subspaces where the total spin has a fixed value. In this regime, and in the isotropic case, we evaluate the characteristic thermalization time analytically, and show that it diverges with the system size in correspondence of the critical points and inside the ferromagnetic region. Quite interestingly, at zero temperature the thermalization time diverges only quadratically with the system size, whereas quantum adiabatic algorithms, aimed at finding the ground state of same system, imply a cubic divergence of the required adiabatic time.