Strong thermalization of the two-component Bose-Hubbard model at finite temperatures

TL;DR

This study demonstrates that a two-component Bose-Hubbard model rapidly reaches thermal equilibrium at finite temperatures, with the entire system's density matrix well approximated by a canonical ensemble after interaction is introduced.

Contribution

It provides evidence that the full density matrix of a two-component Bose-Hubbard system thermalizes, extending understanding beyond simple observables.

Findings

Complete system density matrix thermalizes

Time-averaged density matrix matches canonical ensemble

Thermalization occurs rapidly after interaction onset

Abstract

We study thermalization of a two-component Bose-Hubbard model by exact diagonalization. Initially the two components do not interact and are each at equilibrium but with different temperatures. As the on-site inter-component interaction is turned on, perfect thermalization occurs. Remarkably, not merely those simple "realistic" physical observables thermalize but even the density matrix of the \textit{whole} system---the time-averaged density matrix of the system can be well approximated by that of a canonical ensemble. A conjecture about this fact is put forward.