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 t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio rs = U L/(2t √ πN ) reaches a value r F s ≈ 10, there is a level crossing between ground states of different momenta. Above r F s , the mesoscopic crystallization proceeds through an intermediate regime (r F s < rs < r W s ≈ 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at r F s is avoided and gives rise to a lower threshold r F s (W ) < r F s where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state.PACS. 71.10.-w Theories and models of many-electron systems -73.21.La Quantum dots -73.20.Qt Electron solids

Abstract. A Wigner crystal structure of the electronic ground state is induced by strong Coulomb interactions at low temperature in clean or disordered two-dimensional (2d) samples. For fermions on a mesoscopic disordered 2d lattice, being closed to a torus, we study the persistent current in the regime of strong interaction at zero temperature. We perform a perturbation expansion starting from the Wigner crystal limit which yields power laws for the dependence of the persistent current on the interaction strength. The sign of the persistent current in the strong interaction limit is independent of the disorder realization and strength. It depends only on the electro-statically determined configuration of the particles in the Wigner crystal.

The magnetization of 2d mesoscopic disordered clusters is studied as a function of the Coulomb energy to kinetic energy ratio rs. Between the Fermi system (small rs) and the Wigner molecule (large rs), an intermediate regime is observed where the Wigner antiferromagnetism defavors the Stoner ferromagnetism and where an interaction-induced delocalization of the ground state takes place which is suppressed when the spins are aligned by a parallel magnetic field. The enhancement of the Landé g factor observed in macroscopic systems is reproduced by those mesoscopic systems for similar ratios rs.

We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb repulsion can drive the two particle system to quantum chaos with Wigner-Dyson spectral statistics. For intermediate strengths U of the two repulsions in one dimension, there is a crossover regime where delocalization and spectral rigidity are maximum, whereas the limits of weak and strong U are characterized by a stronger localization and uncorrelated energy levels.Comment: 8 pages, 10 figure

The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb U/r potential. We review a series of exact numerical results obtained in the presence of weak site disorder for fully polarized electrons (spinless fermions) and when the spin degrees of freedom are included. A novel intermediate regime between the Fermi system of weakly interacting localized particles and the correlated Wigner solid is obtained. A detailed analysis of the non disordered case shows that the intermediate ground state is a solid entangled with an excited liquid. For electrons in two dimensions, this raises the question of the existence of an unnoticed intermediate liquid-solid phase. Using the Coulomb energy to kinetic energy ratio rs ∝ U ∝ n −1/2 s