Regular Article

A classical fluctuation theory of the superfluid, Mott, and normal phases of correlated bosons

Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Allahabad 211019, India

^a e-mail: abhishekjoshi@hri.res.in

Received: 24 June 2019
Received in final form: 8 January 2020
Published online: 18 February 2020

Abstract

We present a method that generalises the standard mean field theory of correlated lattice bosons to include amplitude and phase fluctuations of the U(1) field that induces onsite particle number mixing. We solve the resulting problem, initially, by using a classical approximation for the particle number mixing field and a Monte Carlo treatment of the resulting bosonic model. In two dimensions we obtain T_c scales that dramatically improve on mean field theory and are within about 20% of quantum Monte Carlo estimates at density n = 1. The ground state, however, is still mean field, with an overestimate of the critical interaction, U_c, for the superfluid to Mott transition. Further including gaussian quantum fluctuations strikingly improves the U_c and the overall thermal phase diagram. The approach has a computational cost that is linear in system size, readily generalises to multispecies bosons, disorder, and the presence of traps, and yields real frequency response functions.