Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures

TL;DR

This paper investigates the finite temperature effects and out-of-equilibrium dynamics of the one-dimensional Bose-Hubbard model using tensor network methods, confirming Kibble-Zurek scaling at zero temperature and analyzing thermal influences.

Contribution

It applies advanced tensor network techniques to simulate the Bose-Hubbard model at finite temperatures and explores the Kibble-Zurek scaling behavior under quenches.

Findings

Confirmed Kibble-Zurek scaling at zero temperature

Characterized finite temperature effects on dynamics

Provided a simple explanation for thermal behavior

Abstract

We use tensor network methods - Matrix Product States, Tree Tensor Networks, and Locally Purified Tensor Networks - to simulate the one dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. We first explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then, we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite temperature behavior, which we explain by means of a simple argument.