Universal thermodynamics of a two-dimensional Bose gas

TL;DR

This paper demonstrates that the low-temperature thermodynamics of 2D and 3D dilute Bose gases can be described by a universal scaling function, with the 2D case computed via a nonperturbative renormalization group method and validated against experiments.

Contribution

It introduces a universal scaling framework for Bose gas thermodynamics and computes the 2D scaling function using a nonperturbative RG approach, aligning well with experimental data.

Findings

The universal scaling function accurately describes thermodynamics across different dimensions.

The computed BKT transition temperature agrees with quantum Monte Carlo results.

Experimental data for quasi-2D gases match the theoretical predictions.

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 $\calF_d(\mu/k_BT,\tilde g(T))$ 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 $ma_d^2k_BT/\hbar^2$. We compute the scaling function $\calF_2$ using a nonperturbative renormalization-group approach and find that both the $\mu/k_BT$ 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.