Phase transitions of a Bose gas in an optical lattice

TL;DR

This paper investigates phase transitions in ultracold bosonic atoms within an optical lattice, revealing a phase diagram with Mott insulator and Bose-Einstein condensate phases through an exact solution method.

Contribution

It introduces a novel exact solution for the phase diagram of interacting bosons in optical lattices using a large-N limit approach.

Findings

Identification of symmetric and symmetry-broken phases

Exact solution for the phase diagram

Characterization of phase transition types

Abstract

A grand-canonical system of interacting bosons is considered to study phase transitions of ultracold atoms in an optical lattice. The phase diagram is discussed in terms of a matrix-like order parameter, representing a symmetric phase (Mott insulator) and a symmetry-broken phase (Bose-Einstein condensate). An exact solution was found by introducing $N$ colors and taking the limit $N\to\infty$.