The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study

TL;DR

This paper uses high-order symbolic perturbation theory to analytically study the ground state and correlations in the one-dimensional Bose-Hubbard model's Mott insulator phase, aligning well with numerical results.

Contribution

It provides the first high-order analytical expressions for key ground state properties in the 1D Bose-Hubbard model's Mott phase, enhancing understanding and experimental relevance.

Findings

Analytical expressions for ground state energy and correlations.

Good agreement with numerical simulations.

Relevance to ultra cold atomic gas experiments.

Abstract

The one dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high order symbolic perturbative expansion. Analytical expressions are derived for the ground state quantities such as energy per site, variance of on-site occupation, and different correlation functions. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultra cold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.