J. Phys. IV France 12 (2002) Pr9-69
DOI: 10.1051/jp4:20020357

Variational wave function for generalized Wigner lattices in one dimension

S. Fratini¹, B. Valenzuela² and D. Baeriswyl<sup>3

1</sup>  Laboratoire d'Études des Propriétés Électroniques des Solides, CNRS, 25 avenue des Martyrs, BP. 166, 38042 Grenoble cedex 9, France
²  Instituto de Ciencia de Materiales, CSIC, Cantoblanco, 28049 Madrid, Spain
³  Department of Physics, University of Fribourg, Pérolles, 1700 Fribourg, Switzerland

Abstract
We study a system of electrons on a one-dimensional lattice, interacting through the long range Coulomb forces, by means of a variational technique which is the strong coupling analog of the Gutzwiller approach. The problem is thus the quantum version of Hubbard's classical model of the generalized Wigner crystal [J. Hubbard, Phys. Rev. B 17, 494 (1978)]. The magnetic exchange energy arising from quantum fluctuations is calculated, and turns out to be smaller than the energy scale governing charge degrees of freedom. This approach could be relevant in insulating quasi-one-dimensional compounds where the long range Coulomb interactions are not screened. In these compounds charge order often appears at high temperatures and coexists with magnetic order at low temperatures.

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