From independent particle towards collective motion in two electron square lattices

Abstract

The two dimensional crossover from independent particle towards collective motion is studied using 2 spinless fermions interacting via a U/r Coulomb repulsion in a LxL square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation $\Delta r$ of the spacing r between the two particles is larger than the lattice spacing, there is a scaling length $Lo=\sqrt{8}{\pi }^2(t/U)$ such that the relative fluctuation $\Delta r/<r>$ is a universal function of the dimensionless ratio L/Lo, up to finite size corrections of order $L^{-2}$. L<Lo and L>Lo are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U*(L)/t, $\Delta r$ becomes smalller than the lattice spacing, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of (t/U) become valid. A weak random potential reduces the scaling length and favors the correlated motion.

arXiv comment8 pages, 11 figures, to be published in EPJ

Cited by in corpus (2)

• Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder
• Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents