From independent particle towards collective motion for two polarized electrons on a square lattice
CEA/DSM, Service de Physique de l'État Condensé,
Centre d'Études de Saclay, 91191, Gif-sur-Yvette Cedex, France
Corresponding author: a email@example.com
Published online: 19 November 2002
The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a 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 of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length such that the relative fluctuation is a universal function of the dimensionless ratio , up to finite size corrections of order L-2. and 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 , becomes smaller than a, 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.
PACS: 71.10.-w – Theories and models for many-electron systems / 71.27.+a – Strongly correlated electron systems / 73.20.Qt – Electron solids
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002