Simultaneous Diagonal and Off Diagonal Order in the Bose--Hubbard Hamiltonian

TL;DR

This paper uses Quantum Monte Carlo simulations to explore the phase diagram of the Bose-Hubbard model, focusing on the coexistence of superfluid and solid orders, phase separation, and comparison with analytic results.

Contribution

It provides new insights into simultaneous diagonal and off-diagonal order in the Bose-Hubbard model through comprehensive numerical and analytic analysis.

Findings

Identification of regimes with coexisting superfluid and solid order

Observation of phase separation phenomena

Agreement between Monte Carlo results and analytic calculations

Abstract

The Bose-Hubbard model exhibits a rich phase diagram consisting both of insulating regimes where diagonal long range (solid) order dominates as well as conducting regimes where off diagonal long range order (superfluidity) is present. In this paper we describe the results of Quantum Monte Carlo calculations of the phase diagram, both for the hard and soft core cases, with a particular focus on the possibility of simultaneous superfluid and solid order. We also discuss the appearance of phase separation in the model. The simulations are compared with analytic calculations of the phase diagram and spin wave dispersion.