Density Functional Theory for non-relativistic Fermions in the Unitarity Limit

TL;DR

This paper develops an energy density functional for non-relativistic spin-1/2 fermions at unitarity, using epsilon expansion techniques to compute corrections beyond the local density approximation, relevant for trapped fermionic gases.

Contribution

It introduces a novel energy density functional for fermions at unitarity and calculates the leading correction beyond LDA using epsilon expansion around four dimensions.

Findings

Correction coefficient c_s=1.68 at next-to-leading order

Correction term scales as (3N)^(-2/3) for trapped fermions

Significant deviation from non-interacting fermion correction c_s=0.5

Abstract

We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4-epsilon spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=E_(LDA)(1+c_s (3N)^(-2/3)), where E_(LDA) is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c_s=1.68, which is significantly larger than the result for non-interacting fermions, c_s=0.5.