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June  2002, 1(2): 135-159. doi: 10.3934/cpaa.2002.1.135

Peierls instability with electron-electron interaction: the commensurate case

V. Mastropietro 1,

1. 

Dipartimento di Matematica, Università di Roma "Tor Vergata", Roma, I-00133, Italy

Revised  August 2001 Published  March 2002

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 $\frac{\pi}{pF}$ periodic functions, if the interaction is 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 of its reticular structure (Peierls instability). The minima are found solving the Eulero-Lagrange equations of the energy by a contraction method.
Keywords: Quantum statistical physiscs, renormalization group..
Mathematics Subject Classification: 82Dx.
Citation: V. Mastropietro. Peierls instability with electron-electron interaction: the commensurate case. Communications on Pure and Applied Analysis, 2002, 1 (2) : 135-159. doi: 10.3934/cpaa.2002.1.135
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