### Abstract

In this second paper, using N = 3 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 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 r_{s} = UL/(2t√πN). 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.

Original language | English |
---|---|

Pages (from-to) | 87-101 |

Number of pages | 15 |

Journal | European Physical Journal B |

Volume | 33 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2003 |

### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

## Fingerprint Dive into the research topics of 'Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II'. Together they form a unique fingerprint.

## Cite this

*European Physical Journal B*,

*33*(1), 87-101. https://doi.org/10.1140/epjb/e2003-00145-0