Correlation and Magnetic Effects in Narrow Energy Bands. II

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Abstract
Correlation and magnetic effects in narrow bands are studied using a generalized self-consistent cluster treatment of the narrow-band Hamiltonian. Here the dynamics consists of electron hopping between nearest-neighbor sites and Coulomb interaction between electrons on the same site and nearest-neighbor sites. In the simpler case, where the neighbor interactions are neglected, i.e., the Hubbard model, the environment of the cluster is regarded as a particle reservoir, one for each spin. Hopping between the cluster and reservoirs is described by fermion source terms. It is required that the thermodynamic average of the particle currents of each spin within the cluster equal the corresponding particle exchange between cluster and reservoir. Electron motion in the system is examined for varying ratios of the strength of the hopping to the intrasite Coulomb repulsion. A discontinuous transition from an antiferromagnetic insulator to a metal is found under dynamical conditions close to those predicted by Hubbard and Kemeny. The effect of the intersite Coulomb interaction on the transition is next studied. These added terms are seen greatly to influence the transition and the magnetic properties of the cluster.

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