Absence of Wigner molecules in one-dimensional few-fermion systems with short-range interactions

TL;DR

This study uses exact diagonalization to analyze the ground state of few-fermion systems with short-range interactions in one dimension, finding no evidence of Wigner-molecule formation despite density oscillations.

Contribution

It demonstrates that strong short-range interactions do not lead to Wigner-molecule correlations in one-dimensional fermion systems, contrasting with Coulomb-interacting cases.

Findings

Friedel oscillations appear at strong coupling

No Wigner-molecule correlations observed with short-range interactions

Coulomb systems form Wigner molecules at strong coupling

Abstract

We study by means of exact-diagonalization techniques the ground state of a few-fermion system with strong short-range repulsive interactions trapped by a harmonic potential in one spatial dimension. Even when the ground-state density profile displays at strong coupling very well pronounced Friedel oscillations with a `4k_F periodicity', the pair correlation function does not show any signature of Wigner-molecule-type correlations. For the sake of comparison, we present also numerical results for few-electron systems with Coulomb interactions, demonstrating that their ground state at strong coupling is, on the contrary, a Wigner molecule.