Exact Numerical Results on the Ground State of Strongly Interacting Fermi Gases in Two Dimensions

TL;DR

This paper presents exact numerical calculations of the ground state properties of a two-dimensional strongly interacting Fermi gas, providing a new equation of state and detailed physical insights useful for experimental comparisons.

Contribution

The authors introduce a combination of auxiliary-field approaches with force bias techniques to perform large-scale, exact calculations of 2D Fermi gases in the thermodynamic limit, producing a new benchmark equation of state.

Findings

New equation of state for 2D Fermi gases

Systematic determination of pressure, contact, and condensate fraction

Analysis of momentum distribution and pairing correlations

Abstract

Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. A new equation of state is obtained, with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs.~$k_F a$. The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary-fields in determinantal approaches is discussed.