Scaling property of the critical hopping parameters for the Bose-Hubbard model

TL;DR

This paper reveals a scaling law for the critical hopping parameters in the Bose-Hubbard model, showing that mean-field theory closely predicts their dependence on filling factors and providing an accurate approximation formula.

Contribution

The study demonstrates a universal scaling relationship for critical hopping parameters and introduces an accurate approximation formula for various dimensions and filling factors.

Findings

Critical hopping parameters obey a universal scaling law.

Mean-field results nearly fully capture the dependence on filling factor.

An accurate approximation formula for critical parameters is proposed.

Abstract

Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d > 1. We use these data for demonstrating that the critical hopping parameters obey a scaling relationship which allows one to map results for different g onto each other. Unexpectedly, the mean-field result captures the dependence of the exact critical parameters on the filling factor almost fully. We also present an approximation formula which describes the critical parameters for d > 1 and any g with high accuracy.