Phase diagram of harmonically confined one-dimensional fermions with attractive and repulsive interactions

TL;DR

This paper constructs a comprehensive phase diagram for one-dimensional harmonically confined fermions with both attractive and repulsive interactions using density-functional theory, providing analytical expressions and extending previous results.

Contribution

It offers the first complete analytical phase diagram for this system, including new correlation energy interpolation for attractive interactions.

Findings

Confirmed previous numerical results for repulsive interactions.

Derived closed-form expressions for phase boundaries.

Extended phase diagram to attractive interactions with new correlation energy model.

Abstract

We construct the complete $U$-$\mu$ phase diagram for harmonically confined ultracold fermionic atoms with repulsive and attractive interactions. ($\mu$ is the chemical potential and $U$ the interaction strength.) Our approach is based on density-functional theory, and employs analytical expressions for the kinetic and correlation energy functionals. For repulsive interactions our calculations confirm previous numerical studies, and complement these by closed expressions for all phase boundaries and characteristic lines of the phase diagram, and by providing an explanation and solution for difficulties encountered in earlier density-functional work on the same system. For attractive interactions we propose a new and accurate interpolation for the correlation energy, and use it to extend the phase diagram to $U<0$.