Ground-state properties of trapped Bose-Fermi mixtures: role of exchange-correlation

TL;DR

This paper develops a Density Functional Theory approach for inhomogeneous Bose-Fermi mixtures, deriving Kohn-Sham equations and exchange-correlation energies to accurately predict ground-state properties beyond mean-field approximations.

Contribution

It introduces a novel DFT framework for Bose-Fermi mixtures, including exchange-correlation effects, and numerically solves for ground-state properties in trapped systems.

Findings

Exchange-correlation significantly affects stability predictions.

Numerical solutions match experimental density distributions.

Beyond mean-field effects are crucial for accurate modeling.

Abstract

We introduce Density Functional Theory for inhomogeneous Bose-Fermi mixtures, derive the associated Kohn-Sham equations, and determine the exchange-correlation energy in local density approximation. We solve numerically the Kohn-Sham system and determine the boson and fermion density distributions and the ground-state energy of a trapped, dilute mixture beyond mean-field approximation. The importance of the corrections due to exchange--correlation is discussed by comparison with current experiments; in particular, we investigate the effect of of the repulsive potential energy contribution due to exchange--correlation on the stability of the mixture against collapse.