Abstract:
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 L×L 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 a, there is a scaling length L 0 = π2(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L 0, up to finite size corrections of order L-2. L < L 0 and L > L 0 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 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.
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Received 28 March 2002 Published online 19 November 2002
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Martínez, M., Pichard, JL. From independent particle towards collective motion for two polarized electrons on a square lattice. Eur. Phys. J. B 30, 93–100 (2002). https://doi.org/10.1140/epjb/e2002-00362-y
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DOI: https://doi.org/10.1140/epjb/e2002-00362-y