Diagrammatic expansions of Hubbard models

Abstract

Optical lattice are periodic structures made of light, they are formed by the interference of laser beams producing standing waves. The depth and the periodicity of the optical lattice can be highly controlled, therefore, optical lattices provide an ideal framework to study quantum effects. In this project we used diagrammatic techniques to obtain a quasi particle description of an interacting system of electrons in an optical lattice in the basis of Hubbard model.