Symmetry breaking and the order parameters of the Hubbard model

M.R.M.J. Traa, W.J. Caspers

Eike Bick

Roberto Livi, Arianna Montorsi, Mario Rasetti

The effects of different linearization procedures as breaking of the global symmetry of the Hubbard model recently discovered by Yang and Zhang are discussed, together with the ensuing order parameters. In particular it is pointed out how only the Fermi linearization technique allows us both to restore the complete symmetry in the disordered phase, and to describe an ordered phase characterized by an order parameter associated with the breaking of the superconductive symmetry.

T. Schauerte, P. G. J. van Dongen

The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the N\'eel temperature and the order parameter in $d=3$ are smaller than the Hartree-Fock predictions by a factor of $q=0.2599.$ For $d=2$ we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters.

Harald Grosse

Simon Friederich, H. C. Krahl, CHRISTOF WETTERICH

The phases with spontaneously broken symmetries corresponding to antiferromagnetic and $d$-wave superconducting order in the two-dimensional $t\ensuremath{-}{t}^{'}$-Hubbard model are investigated by means of the functional renormalization group. The introduction of composite boson fields in the magnetic, charge density, and superconducting channels allows an efficient parametrization of the four-fermion vertex and the study of regimes where either the antiferromagnetic or superconducting order parameter, or both, are nonzero. We compute the phase diagram and the temperature dependence of the order parameter below the critical temperature, where antiferromagnetic and superconducting order show a tendency of mutual exclusion.