Occupation number and fluctuations in the finite-temperature Bose-Hubbard model

TL;DR

This paper derives analytical formulas for occupation numbers and fluctuations in the finite-temperature Bose-Hubbard model, validated by numerical methods, aiding understanding of thermal effects in cold atom systems.

Contribution

It introduces simple analytical expressions for occupation numbers and fluctuations at finite temperature, bridging Mott-insulator and superfluid regimes, validated by numerical DMRG calculations.

Findings

Analytical formulas closely match numerical results.

High accuracy in the crossover thermal region.

Enables estimation of fluctuations under experimental conditions.

Abstract

We study the occupation numbers and number fluctuations of ultra-cold atoms in deep optical lattices for finite temperatures within the Bose-Hubbard model. Simple analytical expressions for the mean occupation number and number fluctuations are obtained in the weak-hopping regime using an interpolation between results from different perturbation approaches in the Mott-insulator and superfluid phases. These analytical results are compared to exact one dimensional numerical calculations using a finite temperature variant of the Density-Matrix Renormalisation Group (DMRG) method and found to have a high degree of accuracy. We also find very good agreement in the crossover ``thermal'' region. With the present approach the magnitude of number fluctuations under realistic experimental conditions can be estimated and the properties of the finite temperature phase diagram can be studied.