Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions

TL;DR

This paper compares Wigner crystal formation and fermionization in one-dimensional Hubbard models with and without long-range interactions, revealing that long-range interactions are crucial for Wigner crystal signatures.

Contribution

It demonstrates that density peaks alone are insufficient to identify Wigner crystals, emphasizing the role of long-range interactions in their formation.

Findings

Density peaks result from fermionization, not crystallization.

Long-range interactions produce clear Wigner crystal signatures.

Static structure factor confirms Wigner crystal presence with long-range interactions.

Abstract

The ground state properties of Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interaction are investigated by means of the exact diagonalization method. We show that the appearance of $N$-crests in the density profile of a trapped N-fermion system is a natural result of "fermionization" between antiparallel-spin fermions in the strongly repulsive limit and can not be taken as the only signature of Wigner crystal phase, as the static structure factor does not show any signature of crystallization. On the contrary, both the density distribution and static structure factor of Hubbard model with strong long-range interactions display clear signature of Wigner crystal. Our results indicate the important role of long-range interaction in the formation of Wigner crystal.