On the flux phase conjecture at half-filling: an improved proof

TL;DR

This paper simplifies Lieb's proof of the flux phase conjecture for half-filled interacting fermion systems, using a transformation to reflection positive form, and demonstrates its applicability to related models.

Contribution

It provides a simplified proof of the flux phase conjecture and introduces a transformation technique applicable to various fermionic models.

Findings

Simplified proof of the flux phase conjecture at half-filling.

Transformation method to reflection positive form for fermionic Hamiltonians.

Applicability of the method to other models like the $t-V$ and Falicov-Kimball models.

Abstract

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a class of fermionic Hamiltonians into reflection positive form. The method can also be applied to other problems, which we briefly illustrate with two examples concerning the $t-V$ model and an extended Falicov-Kimball model.