Ground state of a partially melted Wigner molecule

TL;DR

This paper investigates the ground state of a three-fermion system on a 2D lattice with Coulomb interactions, revealing a mesoscopic solid-liquid regime during the melting of a Wigner molecule.

Contribution

It introduces a simple ansatz to describe the ground state in the intermediate melting regime of a Wigner molecule on a lattice.

Findings

Formation of a rigid Wigner molecule at high r_s

Existence of a mesoscopic solid-liquid regime during melting

Coexistence of a floppy two-particle molecule with a delocalized particle

Abstract

We consider three spinless fermions free to move on 2d square lattice with periodic boundary conditions and interacting via a U/r Coulomb repulsion. When the Coulomb energy to kinetic energy ratio r_s is large, a rigid Wigner molecule is formed. As r_s decreases, we show that melting proceeds via an intermediate regime where a floppy two particle molecule coexists with a partially delocalized particle. A simple ansatz is given to describe the ground state of this mesoscopic solid-liquid regime.