Finite temperature correlations in the Bose-Hubbard model: application of the Gauge $P$ representation

TL;DR

This paper uses the gauge P representation to simulate finite-temperature correlations in the 1D Bose-Hubbard model, revealing how temperature affects particle number fluctuations and phase boundaries.

Contribution

It introduces a novel application of the gauge P representation to study finite-temperature properties of the Bose-Hubbard model in 1D.

Findings

The stepwise particle number pattern disappears above T ≈ 0.1 U.

Number fluctuations decrease and approach coherent state values as J increases.

A simple relation for the kinetic energy component of the Hamiltonian is established.

Abstract

We study ultracold Bose gases in periodic potentials as described by the Bose-Hubbard model. In 1D and at finite temperature, we simulate ultracold Bose gases in imaginary time with the gauge $P$ representation. We study various quantities including the Luttinger parameter $K$, which is important for locating the boundaries of the Mott insulator lobes, and find a simple relation for the kinetic energy part of the Bose-Hubbard Hamiltonian. We show that for J=0, the stepwise pattern of the average number of particles per lattice site versus the chemical potential vanishes at temperatures above $T \approx 0.1 U$. Also, at chemical potential $\mu=0.5 U$ and temperature $T=0.5 U$ by increasing $J$, the relative value of the number fluctuation decreases and approaches that of a coherent state.