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

Abstract

We construct the complete $U\text{\ensuremath{-}}\ensuremath{\mu}$ phase diagram for harmonically confined ultracold fermionic atoms with repulsive and attractive interactions($\ensuremath{\mu}$ 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, permitting us to obtain closed expressions for all phase boundaries and characteristic lines of the phase diagram, both for repulsive and attractive interactions.