Faculty of Engineering and Natural Sciences
Nonlinear Canonical Transformations Applied to the Study of
Strongly Interacting Electrons
Prof. Dr. Stellan Ostlund
Department of Physics
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. This dilute gas 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 the Shastry-Sutherland lattice, cases where the Mott insulator is not associated with magnetic ordering. The technique can be generalized to insulators with odd valence. For a system of spin-half fermions such as the Hubbard model, the two Fermi degrees of freedom per site will be exactly transformed to a single fermion and an indepdendent spin-like bosonic degree of freedom per site. Computer algebra is an essential tool in carrying out the calculations since the quasiparticles of the dilute Fermi gas are represented in terms of the bare electron operators as complicated composite operators.
February 18, 2010, 11:40 Thursday, FENS 2008