 98510 Bolina O., Marchetti D.H.U.
 The FalicovKimball Model with LongRange Hopping Matrices
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Jul 15, 98

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Abstract. The ground state nature of the FalicovKimball model
with unconstrained hopping of electrons is investigated. We solve the
eigenvalue problem in a pedagogical manner and give a complete account of the
ground state energy both as a function of the number of electrons and nuclei
and as a function of the total number of particles for any value of
interaction $U\in \R $. We also study the energy
gap and show the existence of a phase transition characterized by the
absence of gap at the halffilled band for $U<0$.
The model in consideration was proposed and solved by Farkas\u
ovsky \cite{F} for finite lattices and repulsive onsite interaction $U>0$.
Contrary to his proposal we conveniently scale
the hopping matrix to guarantee the existence of the
thermodynamic limit. We also solve this model with bipartite unconstrained
hopping matrices in order to compare with the KennedyLieb variational
analysis \cite{KL}.
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