Quantum XY criticality in a two-dimensional Bose gas near the Mott transition

TL;DR

This paper derives the universal equation of state for a two-dimensional Bose gas near the Mott transition, highlighting quantum XY criticality and its experimental observability in ultracold gases.

Contribution

It provides a nonperturbative renormalization-group calculation of the equation of state near the multicritical point, confirming universality and comparing with quantum O(2) model results.

Findings

Universal scaling function for pressure near criticality

Agreement with quantum O(2) model calculations

Identification of the critical region in the phase diagram

Abstract

We derive the equation of state of a two-dimensional Bose gas in an optical lattice in the framework of the Bose-Hubbard model. We focus on the vicinity of the multicritical points where the quantum phase transition between the Mott insulator and the superfluid phase occurs at fixed density and belongs to the three-dimensional XY model universality class. Using a nonperturbative renormalization-group approach, we compute the pressure $P(\mu,T)$ as a function of chemical potential and temperature. Our results compare favorably with a calculation based on the quantum O(2) model -- we find the same universal scaling function -- and allow us to determine the region of the phase diagram in the vicinity of a quantum multicritical point where the equation of state is universal. We also discuss the possible experimental observation of quantum XY criticality in a ultracold gas in an optical lattice.