Canonical perturbation theory for inhomogeneous systems of interacting fermions

Abstract

We consider a model of interacting fermions on a lattice with a strong on-site term and a weak intersite one. The model is defined in terms of Hubbard operators and takes into account the local lattice defects as well as the magnetic field. Using a canonical perturbation theory we obtain explicit formulas for parameters of the effective Hamiltonian exact up to second order with respect to the intersite term. We show how the method can be generalized recursively to higher orders and exemplify the procedure with an application to a single band Hubbard model with defects and to its two-orbital extension.