Bose-Hubbard phase diagram with arbitrary integer filling

TL;DR

This paper presents a high-precision method to map the phase diagram of the Bose-Hubbard model at various integer fillings, elucidating the transition between Mott insulator and superfluid phases in different dimensions.

Contribution

It introduces an algorithm based on high-order perturbation series to accurately determine critical parameters for arbitrary integer fillings in the Bose-Hubbard model.

Findings

Accurate critical parameters for Mott insulator to superfluid transition.

Analysis of the approach to mean-field and quantum rotor limits.

Application to both 2D and 3D Bose-Hubbard models.

Abstract

We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities $d > 3$, and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.