Mott Transition in the Hubbard model

TL;DR

This paper explores the metal-insulator transition in the one-dimensional Hubbard model, applying Kohn's criterion, Jordan-Wigner transformation, and analyzing magnetic properties and spin-statistics relations.

Contribution

It provides a detailed analysis of the Mott transition in 1D Hubbard systems, including transformations and magnetic flux effects, with new insights into spin and orbital interactions.

Findings

Bosons prefer zero flux, indicating diamagnetism

Identification of 'happy fluxes' for fermions

Interplay between diamagnetism and spin polarization

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.