Universal thermodynamics of a two-dimensional Bose gas

Using renormalization-group arguments we show that the low-temperature thermodynamics of a three- or two-dimensional dilute Bose gas is fully determined by a universal scaling function ${\text{calF}}_d(\mu \mathrm{/}{k}_{B}T,\tilde{g}(T))$ once the mass $m$ and the s-wave scattering length $a_d$ of the bosons are known ($d$ is the space dimension). Here $\mu$ and $T$ denote the chemical potential and temperature of the gas, and the temperature-dependent dimensionless interaction constant $\tilde{g}(T)$ is a function of $m{a}_d^2{k}_{B}T\mathrm{/}{\mathrm{\hslash }}^2$. We compute the scaling function ${\text{calF}}_2$ using a nonperturbative renormalization-group approach and find that both the $\mu \mathrm{/}{k}_{B}T$ and $\tilde g(T)$ dependencies are in very good agreement with recent experimental data obtained for a quasi-two-dimensional Bose gas with or without optical lattice. We also show that the nonperturbative renormalization-group estimate of the Berezinskii-Kosterlitz-Thouless transition temperature compares well with the result obtained from a quantum Monte Carlo simulation of an effective classical field theory.