Density-functional theory for the spin-1 bosons in a one-dimensional harmonic trap

TL;DR

This paper develops a density-functional theory for one-dimensional spin-1 bosons in a harmonic trap, revealing phase separation and density behaviors influenced by interactions, with implications for experimental observation of exotic pairing.

Contribution

It introduces a novel density-functional approach combining Kohn-Sham equations with Bethe ansatz results for spin-1 bosons in a trap, highlighting phase separation and density non-monotonicity.

Findings

Density distributions depend on interaction parameters.

Phase separation of paired and polarized bosons observed.

Critical polarization identified for exotic pairing.

Abstract

We propose the density-functional theory for one-dimensional harmonically trapped spin-1 bosons in the ground state with repulsive density-density interaction and anti-ferromagnetic spin-exchange interaction. The density distributions of spin singlet paired bosons and polarized bosons with different total polarization for various interaction parameters are obtained by solving the Kohn-Sham equations which are derived based on the local density approximation and the Bethe ansatz exact results for homogeneous system. Non-monotonicity of the central densities is attributed to the competition between the density interaction and spin-exchange. The results reveal the phase separation of the paired and polarized bosons, the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction. We give the R-P phase diagram at strong interaction and find the critical polarization, which paves the way to direct observe the exotic singlet pairing in spinor gas experimentally.