Mott transition in the Hubbard model

Abstract

In this article, I discuss W. Kohn's criterion for a metal insulator transition, within the framework of a one-band Hubbard model. This and related ideas are applied to 1-dimensional Hubbard systems, and some interesting.miscellaneous results discussed. The Jordan-Wigner transformation converting the two species of fermions to two species of hardcore bosons is performed in detail, and the "extra phases" arising from odd-even effects are explicitly derived. Bosons are shown to prefer zero flux (i.e., diamagnetism), and the corresponding "happy fluxes" for the fermions identified. A curious result following from the interplay between orbital diamagnetism and spin polarization is highlighted. A "spin-statistics" like theorem, showing that the anticommutation relations between fermions of opposite spin are crucial to obtain the SU(2) invariance is pointed out.