Quantum quench dynamics of the Bose-Hubbard model at finite temperatures

TL;DR

This paper investigates the dynamics of the Bose-Hubbard model after a sudden change in interaction strength at finite temperature, revealing conditions under which the system thermalizes or relaxes, and examining the distinguishability of evolving and time-averaged states.

Contribution

It provides a detailed analysis of quench dynamics at finite temperature, demonstrating thermalization conditions and the effects of double quenches on state distinguishability.

Findings

Thermalization occurs only in a narrow range of quenched $U$ values.

System relaxes well over a broader range of $U$.

The distinguishability of density matrices depends on the intermediate $U$ value.

Abstract

We study quench dynamics of the Bose-Hubbard model by exact diagonalization. Initially the system is at thermal equilibrium and of a finite temperature. The system is then quenched by changing the on-site interaction strength $U$ suddenly. Both the single-quench and double-quench scenarios are considered. In the former case, the time-averaged density matrix and the real-time evolution are investigated. It is found that though the system thermalizes only in a very narrow range of the quenched value of $U$, it does equilibrate or relax well in a much larger range. Most importantly, it is proven that this is guaranteed for some typical observables in the thermodynamic limit. In order to test whether it is possible to distinguish the unitarily evolving density matrix from the time-averaged (thus time-independent), fully decoherenced density matrix, a second quench is considered. It turns out that the answer is affirmative or negative according to the intermediate value of $U$ is zero or not.