Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons (Communications in Computational Physics, 2006)
Relative to single-band models, multiband models of strongly interactingelectron systems are of growing interest because of their wider range of novel phenomenaand their closer match to the electronic structure of real materials. In this brief reviewwe discuss the physics of three multiband models (the three-band Hubbard, the periodicAnderson, and the Falicov-Kimball models) that was obtained by numerical simulationsat zero temperature. We first give heuristic descriptions of the three principal numericalmethods (the Lanczos, the density matrix renormalization group, and the constrained-path Monte Carlo methods). We then present generalized versions of the models anddiscuss the measurables most often associated with them. Finally, we summarize theresults of their ground state numerical studies. While each model was developed to studyspecific phenomena, unexpected phenomena, usually of a subtle quantum mechanicalnature, are often exhibited. Just as often, the predictions of the numerical simulationsdiffer from those of mean-field theories.
Keywords: Lanczos method; density matrix renormalization group; constrained-path Monte Carlo; three-band Hubbard model; periodic Anderson model; Falicov-Kimball model