Professor Stellan Ostlund
Department of Physics
Gothenburg University
Sweden

Nonlinear canonical transformations applied to the study of strongly interacting electrons.

Abstract:

Exact algebraic transformations that are nonlinear in electron operators naturally map certain strongly interacting Mott insulators with even valence to a dilute gas of Fermi quasiparticles which can can be studied using simple techniques. These ideas have been used to study the Mott insulating phase in the Kondo lattice model and can be used to study the insulating phase in even valence insulators when the insulating phase is not associated with magnetic ordering. The technique can also be generalized to insulators with odd valence. For a system of spin half fermionssuch as the Hubbard model, the two Fermi degrees of freedom persite will be exactly transformed to a single fermion and an indepdendent spin-like bosonic degree of freedom per site incontrast to the even insulators where the transformation is canonical.

Computer algebra is an essential tool in carrying out the calculationssince the quasiparticles of the dilute Fermi gas are represented as complicated composite operators of the bare electron operators.