Density-functional theory for 1D harmonically trapped Bose-Fermi mixture

TL;DR

This paper develops a density-functional theory for a 1D trapped Bose-Fermi mixture with contact interactions, revealing phase separation and fermionization phenomena through numerical solutions of Kohn-Sham equations.

Contribution

It introduces a DFT approach combining Bethe ansatz solutions and local density approximation for 1D Bose-Fermi mixtures, capturing strong correlation effects.

Findings

Fermions are expelled from the trap center at strong interactions.

Oscillations in Bose density indicate strong Bose-Fermi correlations.

Ground state energy matches fermionization limit at infinite interaction.

Abstract

We present a density-functional theory for the one dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the Local Density Approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for strong enough interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in the Bose density curves reflecting the strong correlation with Fermions. For infinite strong interaction, the ground state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.