On the different types of states of a one dimensional system of electrons in the Hartree-Fock method

Abstract

We consider the different types of ground states of one-dimensional lattice gas of electrons. Interactions between electrons on the same lattice point and on neighboring lattice points are taken into account. The treatment is based on Hartree-Fock approximation for an unbounded system. Regions of the parameter space of the electron-electron interaction are found corresponding to the existence of mixed solutions (i.e., diagonal and nondiagonal long-range order are present stimultaneously). It is shown that the ground state of the system always corresponds to one of the pure types of order (only diagonal or only nondiagonal long-range order) and that diagonal order is present in the ground state. Conditions for the stability of the pure solutions against various perturbations are found.