Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices

TL;DR

This paper develops a collective quantum field theory for 3D bosonic optical lattices, predicting critical temperature behavior and quantum phase transitions, with results aligning with some experimental observations.

Contribution

It introduces a mean-field and variational perturbation approach to analyze phase transitions in 3D bosonic lattices, contrasting previous predictions about superfluid states.

Findings

Mean-field approximation captures critical temperature dependence.

Predicts a second-order quantum phase transition.

Finds no superfluid state with zero condensate fraction.

Abstract

We formulate the Collective Quantum Field Theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Fred Cooper et al. and in a lowest-order Variational Perturbation Theory (VPT). It is shown that present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second - order quantum phase transition.In contrast to a recent prediction for atomic gases by Fred Cooper et. al., we find no superfluid state with zero condensate fraction.