Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions

TL;DR

This paper investigates the universal critical behavior of 2D bosonic gases at the BKT transition using quantum Monte Carlo simulations, providing precise critical temperature estimates and confirming universality in trapped cold atom systems.

Contribution

It introduces a reliable finite-size scaling method for determining the BKT critical temperature and verifies universality in trapped systems, relevant for cold atom experiments.

Findings

Accurate determination of the BKT critical temperature using a novel matching method.

Confirmation of universality in trap-size dependence at the BKT transition.

Quantum Monte Carlo simulations of the hard-core Bose-Hubbard model at zero chemical potential.

Abstract

We study the universal critical behavior of two-dimensional (2D) lattice bosonic gases at the Berezinskii-Kosterlitz-Thouless (BKT) transition, which separates the low-temperature superfluid phase from the high-temperature normal phase. For this purpose, we perform quantum Monte Carlo simulations of the hard-core Bose-Hubbard (BH) model at zero chemical potential. We determine the critical temperature by using a matching method that relates finite-size data for the BH model with corresponding data computed in the classical XY model. In this approach, the neglected scaling corrections decay as inverse powers of the lattice size L, and not as powers of 1/lnL, as in more standard approaches, making the estimate of the critical temperature much more reliable. Then, we consider the BH model in the presence of a trapping harmonic potential, and verify the universality of the trap-size dependence at the BKT critical point. This issue is relevant for experiments with quasi-2D trapped cold atoms.