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

¹ James Franck Institute and Department of Physics, University of Chicago - Chicago, IL 60637, USA
² Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, Université Pierre et Marie Curie 4 Place Jussieu, 75252 Paris Cedex 05, France

Received: 12 July 2013
Accepted: 1 October 2013

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(μ, 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 an ultracold gas in an optical lattice.