Quantum States of Matter of Simple Bosonic Systems: BEC's, Superfluids and Quantum Solids

TL;DR

This paper analyzes the phase diagram of a single-component Bose system in a lattice at zero temperature, identifying conditions for Mott insulator and superfluid phases and characterizing the nature of the phase transition.

Contribution

It provides a variational calculation of the energies for Mott insulator and superfluid phases, revealing the conditions for phase stability and the discontinuous nature of the transition.

Findings

Mott insulator is stable below a critical density depending on lattice well depth.

The phase transition between superfluid and Mott insulator is discontinuous.

The transition occurs regardless of commensurability of boson number with the lattice.

Abstract

The phase diagram of a single component Bose system in a lattice at zero temperature is obtained. We calculate the variational energies for the Mott insulating and superfluid phases. Below a certain critical density, which depends monotonically on the well depth of the lattice, the Mott insulating phase is stable over the superfluid phase for low enough tunelling amplitude regardless of whether the number of bosons is or is not incommensurate with the lattice. The transition is discontinuous as the superfluid order parameter jumps from a finite value to zero at the Mott transition.