ON THE FLUX PHASE CONJECTURE AT HALF-FILLING - AN IMPROVED PROOF

We present a simplification of Lieb's proof of the flux phase conjectu re for interacting Fermion systems-such as the Hubbard model-at half-f illing on a general class of graphs. The main ingredient is a procedur e which transforms a class of fermionic Hamiltonians into reflection-p ositive form. The method can also be applied to other problems, which we briefly illustrate with two examples concerning the t-V model and a n extended Falicov-Kimball model.