Thermal phases of correlated lattice boson: a classical fluctuation theory

TL;DR

This paper develops a classical fluctuation theory for correlated lattice bosons that improves the accuracy of critical temperature predictions over mean field theory, aligning closer to quantum Monte Carlo results.

Contribution

It introduces a method extending mean field theory to include amplitude and phase fluctuations via an auxiliary field, enhancing predictions of thermal phase transitions in lattice bosons.

Findings

Improved critical temperature estimates within 20% of quantum Monte Carlo.

Enhanced critical interaction U_c estimates with quantum fluctuation corrections.

Method is computationally efficient and adaptable to multispecies bosons and trapping potentials.

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. This arises formally from an auxiliary field decomposition of the kinetic term in a Bose Hubbard model. 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 full quantum Monte Carlo estimates. The `classical approximation' ground state, however, is still mean field, with an overestimate of the critical interaction, $U_c$, for the superfluid to Mott transition. By further including low order quantum fluctuations in the free energy functional we improve significantly on the $U_c$, and the overall thermal phase diagram. The classical approximation based method has a computational cost linear in system size. The methods readily generalise to multispecies bosons and the presence of traps.