Critical temperature of interacting Bose gases in two and three dimensions

TL;DR

This study uses large-scale Path Integral Monte Carlo simulations to determine the superfluid transition temperature of interacting Bose gases in two and three dimensions, revealing the limits of universality and clarifying discrepancies in previous research.

Contribution

It provides the first comprehensive analysis of the critical temperature in 2D and 3D Bose gases with detailed potential models and large particle numbers, clarifying the universality limits and discrepancies in prior studies.

Findings

Universality in 3D sets in at gas parameter $na^3 \,\lesssim\, 10^{-4}$.

The asymptotic expansion validity limit is $na^3 \,\lesssim\, 10^{-6}$.

Good agreement with classical $|\,\psi|^4$ model in 2D up to high densities.

Abstract

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale Path Integral Monte Carlo simulations (with up to $N=10^5$ particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter $na^3 \lesssim 10^{-4}$. This value is different from the estimate $na^3 \lesssim 10^{-6}$ for the validity of the asymptotic expansion in the limit of vanishing $na^3$. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice $|\psi|^4$ model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.