Eur. Phys. J. B 33, 87-101 (2003)
https://doi.org/10.1140/epjb/e2003-00145-0

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

¹ CEA/DSM, Service de Physique de l'État Condensé, Centre d'Études de Saclay, 91191 Gif-sur-Yvette Cedex, France
² Eötvös University, Departement of Physics of Complex Systems, 1117 Budapest, Pázmány Péter sétány 1/A, Hungary
³ Laboratoire de Physique Théorique et Modélisation, Universtité de Cergy-Pontoise, 95031, Cergy-Pontoise Cedex, France

Corresponding author: ^a jpichard@cea.fr

Received: 22 October 2002
Published online: 23 May 2003

Abstract

In this second paper, using N=3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio . This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L=6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime.