From independent particle towards collective motion in two electron square lattices

Details From independent particle towards collective motion in two electron square lattices From independent particle towards collective motion in two electron square lattices

2002-03-28

arxiv.org/abs/cond-mat/0203579v1

Physics

Condensed Matter

Strongly Correlated Electrons

8 pages, 11 figures, to be published in EPJ

Scientific paper

10.1140/epjb/e2002-00362-y

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 $\Delta r/$ is a universal function of the dimensionless ratio L/Lo, up to finite size corrections of order $L^{-2}$. LLo 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.

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