# Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations

## TL;DR

This paper demonstrates that the critical points of the 3D Bose-Hubbard model can be precisely identified using the derivative of on-site atom number fluctuations, which are experimentally accessible, and extracts critical exponents through finite-size scaling.

## Contribution

It introduces a method to accurately locate quantum critical points using atom number fluctuation derivatives and validates it with Quantum Monte Carlo simulations.

## Key findings

- Precise determination of critical points for superfluid-Mott insulator transition.
- Extraction of the correlation-length critical exponent from fluctuation data.
- Applicability of the method to experimentally measured quantities like time-of-flight images.

## Abstract

We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of the variance, with respect to the parameter driving the transition, has a pronounced maximum close to critical points. We show that Quantum Monte Carlo studies of this maximum lead to precise determination of critical points for the superfluid-Mott insulator transition in systems with mean number of atoms per lattice site equal to one, two, and three. We also extract from such data the correlation-length critical exponent through the finite-size scaling analysis and discuss how the derivative of the variance can be reliably computed from numerical data for the variance. The same conclusions apply to the derivative of the nearest-neighbor correlation function, which can be obtained from routinely measured time-of-flight images.