Universal thermodynamics of a two-dimensional Bose gas

Abstract

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 $\calF_d(μ/k_BT,\tilde g(T))$ 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 $m{a}_d^2{k}_{B}T/{\hslash }^2$. We compute the scaling function $\calF_2$ using a nonperturbative renormalization-group approach and find that both the $\mu /k_{B}T$ 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.

arXiv comment17 pages, 18 figures, published version

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