Exact few-body results for strongly correlated quantum gases in two dimensions

TL;DR

This paper provides exact solutions for two- and three-body strongly correlated quantum gases in two dimensions, linking few-body physics to many-body thermodynamics and offering benchmarks for experiments and simulations.

Contribution

It introduces exact two- and three-body solutions for 2D quantum gases with arbitrary scattering length, connecting few-body results to high-temperature many-body properties.

Findings

Calculated second and third virial coefficients for strongly interacting Fermi gases.

Analyzed high-temperature thermodynamics of 2D Fermi gases using exact energy spectra.

Provided benchmarks for quantum Monte Carlo simulations.

Abstract

The study of strongly correlated quantum gases in two dimensions has important ramifications for understanding many intriguing pheomena in solid materials, such as high-$T_{c}$ superconductivity and the fractional quantum Hall effect. However, theoretical methods are plagued by the existence of significant quantum fluctuations. Here, we present two- and three-body exact solutions for both fermions and bosons trapped in a two-dimensional harmonic potential, with an arbitrary $s$-wave scattering length. These few-particle solutions link in a natural way to the high-temperature properties of many-particle systems via a quantum virial expansion. As a concrete example, using the energy spectrum of few fermions, we calculate the second and third virial coefficients of a strongly interacting Fermi gas in two dimensions, and consequently investigate its high-temperature thermodynamics. Our thermodynamic results may be useful for ongoing experiments on two-dimensional Fermi gases. These exact results also provide an unbiased benchmark for quantum Monte Carlo simulations of two-dimensional Fermi gases at high temperatures.