Locating the quantum critical point of the Bose-Hubbard model through singularities of simple observables

TL;DR

This paper presents a simple method to locate the quantum critical point in the 2D Bose-Hubbard model by analyzing singularities in observable derivatives, which can be applied to experimental cold atom systems.

Contribution

It introduces a straightforward approach using observable derivatives to accurately determine the critical point in the Bose-Hubbard model, extendable to other Hubbard-like systems.

Findings

Derivatives of on-site atom number fluctuations are singular at the critical point.

Nearest-neighbor two-point correlation functions also show singular behavior at the transition.

The method accurately locates the critical point in quantum Monte Carlo simulations.

Abstract

We show that the critical point of the two-dimensional Bose-Hubbard model can be easily found through studies of either on-site atom number fluctuations or the nearest-neighbor two-point correlation function (the expectation value of the tunnelling operator). Our strategy to locate the critical point is based on the observation that the derivatives of these observables with respect to the parameter that drives the superfluid-Mott insulator transition are singular at the critical point in the thermodynamic limit. Performing the quantum Monte Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this technique leads to the accurate determination of the position of its critical point. Our results can be easily extended to the three-dimensional Bose-Hubbard model and different Hubbard-like models. They provide a simple experimentally-relevant way of locating critical points in various cold atomic lattice systems.