Hartree-Fock theory of spiral magnetic order in the 2-d Hubbard model

Abstract

The magnetic order in the 2-d Hubbard model is investigated within Hartree-Fock theory. For the class of states with uniform particle density and spiral arrangement of spins the phase diagram is obtained by minimizing the free energy. At zero temperature and large Hubbard interactionU there is a continuous transition from the antiferromagnetic solution at half filling over a spiral state of increasing wavelength along the diagonal of the lattice to the ferromagnetic state at doping δ_c ≈ 2t/U. At finite temperatureT, the antiferromagnetic state remains stable for doping smaller than δ_AF ≈ 2T/U. For intermediate values ofU and finite doping there exists also a phase with a spiral wave vector of the form Q=(Q, π).