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 $|\ensuremath{\psi}{|}^{4}$ model on a lattice. The critical density and chemical potential are given by relations ${n}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(mT/2\ensuremath{\pi}{\ensuremath{\Elzxh}}^{2})\mathrm{ln}(\ensuremath{\xi}{\ensuremath{\Elzxh}}^{2}/mU)$ and ${\ensuremath{\mu}}_{c}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(mTU/\ensuremath{\pi}{\ensuremath{\Elzxh}}^{2})\mathrm{ln}({\ensuremath{\xi}}_{\ensuremath{\mu}}{\ensuremath{\Elzxh}}^{2}/mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $\ensuremath{\xi}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}380\ifmmode\pm\else\textpm\fi{}3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For ${\ensuremath{\xi}}_{\ensuremath{\mu}}$ our result is ${\ensuremath{\xi}}_{\ensuremath{\mu}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}13.2\ifmmode\pm\else\textpm\fi{}0.4$. We also report the study of the quasicondensate correlations at the critical point.