Abstract
We consider the static Holstein model, describing a chain of fermions interacting with a classical phonon field, when the interaction is weak and the density is a rational number p = P/Q, with P, Q relative prime integers. We show that the energy of the system, as a function of the phonon field, has one (if Q is even) or two (if Q is odd) stationary points, defined up to a lattice translation, which are local minima in the space of fields periodic with period equal to the inverse of the density.
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Benfatto, G., Gentile, G. & Mastropietro, V. Peierls Instability for the Holstein Model with Rational Density. Journal of Statistical Physics 92, 1071–1113 (1998). https://doi.org/10.1023/A:1023052812507
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DOI: https://doi.org/10.1023/A:1023052812507