Study of the Mott Transition in the Three-Dimensional Hubbard Model

Abstract

The Mott-Hubbard transition in the three-dimensional Hubbard model is studied by means of the composite operator method. Analytical and numerical calculations show the existence of a critical value U c of the Coulomb interaction which separates paramagnetic insulating and metallic phases. In the composite operator method the ratio U c /W, where W is the band width, has the same value as in the two-dimensional case. The ground state of the Mott insulator is characterized by a local antiferromagnetic order where the electrons keep some mobility, but this latter must be compatible with the local ordering. By analyzing the intersite hopping it is possible to establish that some correlation functions behave as order parameters in the insulating phase.