Broken symmetries and the overhauser model

G. Kuti, G. Marx

E.M. Henley, Th.W. Ruijgrok

Douglas J. Klein

Shiwei Zhang, David M. Ceperley

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.

Heide Narnhofer, Walter E Thirring

M. Broidioi, Bruno Nachtergaele, André F. Verbeure

A Goldstone-type theorem is derived to reveal the nature of the spontaneous symmetry breaking occurring in the Overhauser model. Explicit expressions for the equilibrium states of the model are calculated. The fluctuations of the fields satisfy a central limit theorem. The limit is a new set of Fermionic fields that inherit their dynamics from the original model. In the low-temperature phase, where the order parameter does not vanish, this dynamics is nontrivial and basically shows oscillations with a frequency related to the order parameter.