Heavy-fermion system: An exact many-body solution to a periodic-cluster Hubbard model

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Abstract
An exact solution of an eight-site crystal model with periodic boundary conditions, a small face-centered-cubic crystal, is presented for the case of a heavy-fermion system. The model consists of (a) a single, fully symmetric orbital per site, with nearest-neighbor and second-nearest-neighbor hopping, (b) an infinite Coulomb repulsion between electrons on the same site, (c) antiferromagnetic superexchange interactions, and (d) a nearly-half-filled band ((7/8 electron per site). Application of group-theoretical techniques yields a set of energies which are at most (analytic) solutions of quadratic equations. Depending on the sign of the nearest-neighbor hopping parameter the ground state exhibits either a huge accidental degeneracy (the heavy-fermion case), or simple, uniform, saturated itinerant ferromagnetism. The model is, at once, easy to handle and yet rich in structure. Fermi-surface, spin-wave, and electron-transport properties are investigated, and consequences for real systems discussed.