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From independent particle towards collective motion in two electron square lattices

Moises Martinez·Jean-Louis Pichard
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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 $Δr$ of the spacing r between the two particles is larger than the lattice spacing, there is a scaling length $Lo=\sqrt{8}π^2(t/U)$ such that the relative fluctuation $Δr/ $ is a universal function of the dimensionless ratio L/Lo, up to finite size corrections of order $L^{-2}$. 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, $Δr$ 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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Moises Martinez, Jean-Louis Pichard. 2002-03-28. From independent particle towards collective motion in two electron square lattices. https://doi.org/10.1140/epjb%2Fe2002-00362-y

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