Correlation and Magnetic Effects in Narrow Energy Bands

Correlation and magnetic effects in narrow bands are studied using a new type of self‐consistent cluster treatment of Hubbard's Hamiltonian. Here the dynamics consist of electron hopping between lattice sites and Coulomb repulsion between electrons only on the same site. The environment of the cluster is regarded as a particle reservoir, one such 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 Coulomb repulsion. This is done as a function of electron density, spin, temperature, and external magnetic field. A Mott transition is found under dynamical conditions close to those predicted by Hubbard when there is one particle per site. For $\text{〈n〉\hspace{0.17em}≠\hspace{0.17em}1}$ , no metal insulator transition exists although discontinuous changes in the cluster‐reservoir coupling occur. The magnetic susceptibility of the cluster reveals antiferromagnetic behavior for $\text{〈n〉\hspace{0.17em}=\hspace{0.17em}1}$ , ferromagnetic behavior for $\text{〈n〉\hspace{0.17em}>\hspace{0.17em}1}$ , and partial ferromagnetic character for $\text{n\hspace{0.17em}<\hspace{0.17em}1}$ . This appears to agree with Nagoaka's results.