To appear in Comm. Pure Applied Analysis4

Author: V. Mastropietro

Title: Peierls istability with electron-electron interaction: the commensurate case

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

key words: Interacting Fermions, Peierls instability.

Vieri Mastropietro

Universita' di Roma 2, Dip. Matematica

Via Fontanile di Carcaricola

00133 Roma, Italia