Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice I

TL;DR

This paper revisits the concept of a supersolid phase for a small number of polarized electrons on a 2D square lattice, exploring the phase transition between quantum liquid and solid states.

Contribution

It provides a detailed analysis of the supersolid phase for spinless fermions on a lattice, extending the original Andreev-Lifshitz conjecture to a lattice model.

Findings

Identification of conditions for supersolid formation

Characterization of phase transition between liquid and solid

Insights into electron interactions on a lattice

Abstract

In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L * L square lattice with periodic boundary conditions and nearest neighbor hopping.