Quantum phase transitions in optical lattices beyond Bogoliubov approximation

TL;DR

This paper investigates quantum phase transitions in optical lattices using a two-loop variational perturbation theory approach, surpassing simpler approximations to accurately describe the superfluid to Mott insulator transition.

Contribution

It introduces a two-loop approximation method within variational perturbation theory to better model quantum phase transitions in optical lattices, improving upon traditional Bogoliubov and Hartree-Fock-Popov methods.

Findings

Successfully reproduces superfluid-Mott insulator transition

Analyzes superfluid fraction and ground state energy

Demonstrates improved accuracy over simpler approximations

Abstract

We study the quantum phase transition in optical lattices using ordinary Bose Hubbard Hamiltonian within two loop approximation in variational perturbation theory. We have shown that this approximation can reproduce superfluid Mott insulator transition in contrast to the simple Bogoliubov or Hartee - Fock - Popov approximations. The superfluid fraction and ground state energy per particle vs input parameters of the model are studied.