Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model

TL;DR

This paper presents high-precision quantum Monte Carlo simulations of the 3D Bose-Hubbard model, accurately determining critical parameters, excitation properties, and thermodynamic behaviors relevant for experiments and quantum information applications.

Contribution

It provides the most accurate critical point, gap, and excitation parameters for the 3D Bose-Hubbard model to date, aiding experimental and theoretical studies.

Findings

Critical point at (U/t)_c = 29.34(2) for n=1

Measured insulating gap Delta with a few percent accuracy

Derived thermodynamic curves for specific heat and entropy

Abstract

We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantly higher accuracy than it has been done in the past. In particular, the position of the critical point at filling factor n=1 is found to be at (U/t)_c = 29.34(2), and the insulating gap Delta is measured with accuracy of a few percent of the hopping amplitude t. We obtain the effective mass of particle and hole excitations in the insulating state--with explicit demonstration of the emerging particle-hole symmetry and relativistic dispersion law at the transition tip--along with the sound velocity in the strongly correlated superfluid phase. These parameters are the necessary ingredients to perform analytic estimates of the low temperature (T << Delta) thermodynamics in macroscopic samples. We present accurate thermodynamic curves, including these for specific heat and entropy, for typical insulating (U/t=40) and superfluid (t/U=0.0385) phases. Our data can serve as a basis for accurate experimental thermometry, and a guide for appropriate initial conditions if one attempts to use interacting bosons in quantum information processing.