Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

Abstract

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical $|ψ|^4$-model on a lattice. The critical density and chemical potential are given by relations $n_c=(mT/2π\hbar^2) \ln(ξ\hbar^2/ mU)$ and $μ_c=(mTU/π\hbar^2) \ln(ξ_μ \hbar^2/ mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $ξ= 380 \pm 3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For $ξ_μ$ our result is $ξ_μ = 13.2 \pm 0.4 $. We also report the study of the quasi-condensate correlations at the critical point.