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Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents

Houman Falakshahi·Zoltan Adam Nemeth·Jean-Louis Pichard
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Abstract

For an interacting system of N electrons, we study the conditions under which a lattice model of size L with nearest neighbor hopping t and U/r Coulomb repulsion has the same ground state as a continuum model. For a fixed value of N, one gets identical results when the inter-electron spacing to the Bohr radius ratio r_s < r_s^*. Above r_s^*, the persistent current created by an enclosed flux begins to decay and r_s ceases to be the scaling parameter. Three criteria giving similar r_s^* are proposed and checked using square lattices.

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Houman Falakshahi, Zoltan Adam Nemeth, Jean-Louis Pichard. 2003-05-27. Effect of a lattice upon an interacting system of electrons: Breakdown of scaling and decay of persistent currents. https://arxiv.org/abs/cond-mat/0305619

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