Quantitative Studies on the Quantum Critical Regime near Superfluid to Mott Insulator Transition

TL;DR

This paper uses quantum Monte Carlo simulations to analyze the critical behaviors near the superfluid to Mott insulator transition in a 2D optical lattice, identifying the extent of the universal critical regime.

Contribution

It provides a quantitative determination of the critical regime for quantum and classical transitions, aligning numerical results with effective theory predictions.

Findings

Critical regime extends over a few lattice sites.

Universal scaling behaviors are observable in current experiments.

Quantitative agreement between simulations and theory.

Abstract

We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those given by the effective theory, we quantitatively determine the critical regime where the universal scaling behaviors applies for both classical Berezinskii-Kosterlitz-Thouless transition at a finite temperature and quantum phase transition from superfluid to Mott insulator. Our results show that the critical regime can be as large as a few lattice sites in optical lattice and should be observable in present experimental conditions.