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 intersting 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.

15 pages

Cited by in corpus (5)

• Spin-Charge Separation in the $t-J$ Model: Magnetic and Transport Anomalies
• Seven Useful Questions in Density Functional Theory
• Phase Diagram of a Model of Correlated Hopping of Electrons in a Lattice of Berry Molecules
• Non-equilibrium vortex annealing of structural disorder in Berezinskii-Kosterlitz-Thouless dynamics of two-dimensional XY-model
• Drude weight and total optical weight in a t-t'-J model