Peierls instability with electron-electron interaction: the commensurate case

Abstract

We consider a quantum many-body model describing a system ofelectrons interacting with themselves and hopping from one ion to another of aone dimensional lattice. We show that the ground state energy of such system,as a functional of the ionic configurations, has local minima in correspondenceof configurations described by smooth $\frac{\pi}{pF}$periodic functions, if the interactionis repulsive and large enough and pF is the Fermi momentum of the electrons.This means physically that a $d=1$ metal develop a periodic distortion ofits reticular structure (Peierls instability). The minima are found solving theEulero-Lagrange equations of the energy by a contraction method.