Critical temperature of interacting Bose gases in two and three dimensions

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 $n{a}^3\lesssim 10^{-4}$. This value is different from the estimate $n{a}^3\lesssim 10^{-6}$ for the validity of the asymptotic expansion in the limit of vanishing $n{a}^3$. 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.

4 pages, 5 figures

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• Berezinskii-Kosterlitz-Thouless Crossover in a Trapped Atomic Gas
• Critical Point of an Interacting Two-Dimensional Atomic Bose Gas
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• Equation of state of an interacting Bose gas at finite temperature: a Path Integral Monte Carlo study

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