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

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.