Density-functional theory for fermions in the unitary regime

TL;DR

This paper develops a density functional approach within Kohn-Sham theory to study strongly interacting fermions in the unitary regime, accurately estimating the universal constant and effective mass by fitting to solvable models.

Contribution

It introduces a simple density functional parametrized by an effective mass and the universal constant, fitted to exactly solvable two-body problems, for fermions in the unitary regime.

Findings

Estimated the universal constant ξ as 0.42

Determined a large effective mass for the system

Validated approach using the Calogero model

Abstract

In the unitary regime, fermions interact strongly via two-body potentials that exhibit a zero range and a (negative) infinite scattering length. The energy density is proportional to the free Fermi gas with a proportionality constant $\xi$. We use a simple density functional parametrized by an effective mass and the universal constant $\xi$, and employ Kohn-Sham density-functional theory to obtain the parameters from fit to one exactly solvable two-body problem. This yields $\xi=0.42$ and a rather large effective mass. Our approach is checked by similar Kohn-Sham calculations for the exactly solvable Calogero model.