Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement

TL;DR

This paper develops a Bethe-Ansatz spin-density functional method to study the ground-state properties of repulsive spin-1/2 fermions in a one-dimensional harmonic trap, revealing antiferromagnetic quasi-order formation.

Contribution

It introduces a new functional approach that accurately models many-fermion systems and captures magnetic ordering phenomena in one dimension.

Findings

Accurately reproduces exact solutions for two-fermion systems.

Shows formation of antiferromagnetic quasi-order with increasing interaction strength.

Provides a high-precision density profile for many-fermion systems.

Abstract

A Bethe-Ansatz spin-density functional approach is developed to evaluate the ground-state density profile in a system of repulsively interacting spin-1/2 fermions inside a quasi-one-dimensional harmonic well. The approach allows for the formation of antiferromagnetic quasi-order with increasing coupling strength and reproduces with high accuracy the exact solution that is available for the two-fermion system.