GROUND-STATES AND LOW-TEMPERATURE PHASES OF ITINERANT ELECTRONS INTERACTING WITH CLASSICAL FIELDS - A REVIEW OF RIGOROUS RESULTS

We review, from a unified point of view, a general class of models of itinerant electrons interacting with classical fields. Applications to the static Holstein, Kondo, and Hubbard models are discussed. The gro und state structure of the classical field is investigated when the el ectron band is half-filled. Some of the results are also valid when th ere is a Hubbard interaction between spin up and spin down electrons. It is found that the ground states are either homogeneous or period tw o Neel configurations, depending on the geometry of the lattice and on the magnetic fluxes present in the system. In the specific models, Ne el configurations correspond to Peierls, magnetic or superconducting i nstabilities of the homogeneous state. The effect of small thermal and quantum fluctuations of the classical fields are reviewed in the cont ext of the Holstein model. Many of the results described here originat e from the work of Elliott Lieb and collaborators. (C) 1997 American I nstitute of Physics.