Variational Wave Function for Generalized Wigner Lattices in One Dimension

TL;DR

This paper introduces a variational wave function approach to study one-dimensional electron systems with long-range Coulomb interactions, revealing insights into charge and magnetic order in quasi-one-dimensional insulators.

Contribution

It develops a strong coupling variational method analogous to Gutzwiller's approach for analyzing generalized Wigner lattices in 1D systems.

Findings

Magnetic exchange energy is smaller than charge energy scale.

Method applicable to insulating quasi-1D compounds with unscreened Coulomb interactions.

Charge order can coexist with magnetic order at low temperatures.

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.