A lattice pairing-field approach to ultracold Fermi gases

TL;DR

This paper introduces a pairing-field formalism for lattice studies of ultracold Fermi gases, enabling detailed analysis of their phase structure and pair correlations, demonstrated through a one-dimensional case using complex Langevin methods.

Contribution

The paper presents a novel pairing-field formalism for ab initio lattice studies of ultracold Fermi gases, facilitating analysis of phase behavior and pair correlations.

Findings

Computed density equation of state for 1D Fermi gas.

Determined superfluid order parameter in 1D Fermi system.

Applied complex Langevin to overcome sign problem.

Abstract

We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a $(d\!+\!1)$-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components can be described by the exchange of a corresponding pairing field. The introduction of a pairing field may indeed be convenient for studies of, e.g., the finite-temperature phase structure and critical behavior of, e.g., ultracold atomic Fermi gases. Moreover, such a formalism allows to directly compute the momentum and frequency dependence of the pair propagator, from which the pair-correlation function can be extracted. For a first illustration of the application of our formalism, we compute the density equation of state and the superfluid order parameter for a gas of unpolarized fermions in $(0\!+\!1)$ dimensions by employing the complex Langevin approach to surmount the sign problem.