Quantum critical properties of Bose-Hubbard models

TL;DR

This paper investigates quantum critical properties of the Bose-Hubbard model at the Mott insulator-to-superfluid transition, using advanced numerical methods to analyze phase boundaries and correlation functions in various lattice geometries.

Contribution

It introduces a combined high-order perturbation and hypergeometric analytic continuation approach to accurately characterize phase boundaries and critical exponents in Bose-Hubbard models.

Findings

Confirmed the divergence exponent inequality for correlation functions.

Provided precise parametrizations of phase boundaries at Mott lobe tips.

Supported the criticality condition sharpening the inequality to equality.

Abstract

The Mott insulator-to-superfluid transition exhibited by the Bose-Hubbard model on a two-dimensional square lattice occurs for any value of the chemical potential, but becomes critical at the tips of the so-called Mott lobes only. Employing a numerical approach based on a combination of high-order perturbation theory and hypergeometric analytic continuation we investigate how quantum critical properties manifest themselves in computational practice. We consider two-dimensional triangular lattices and three-dimensional cubic lattices for comparison, providing accurate parametrizations of the phase boundaries at the tips of the respective first lobes. In particular, we lend strong support to a recently suggested inequality which bounds the divergence exponent of the one-particle correlation function in terms of that of the two-particle correlation function, and which sharpens to an equality if and only if a system becomes critical.