Interplay of superconductivity and magnetism in strong coupling

A model is introduced describing the interplay between superconductivity an d spin ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. Due to a special cho ice for the lattice, this model has a strong-coupling limit when the superc onductivity can be described by a bosonic theory, similar to the strongly c oupled negative U Hubbard model. This limit is analyzed in the present pape r. A rich mean-field phase diagram is found and the leading quantum correct ions to the mean-field results are calculated. The first-order line between the antiferromagnetic and the superconducting phase is found to terminate at a bicritical point, where two second-order lines originate. At these lin es, the system undergoes a transition to and from a phase exhibiting both a ntiferromagnetic order and superconductivity. Pit finite temperatures above the spin-disordering line, quantum-critical behavior is found. For specifi c values of the model parameters, it is possible to obtain SO(5) symmetry i nvolving the spin and the phase sector at the tricritical point. Although t his symmetry is explicitly broken by the projection to the lower Hubbard ba nd, it survives on the mean-field level, and modes related to a spontaneous ly broken SO(5) symmetry are present on the level of the random phase appro ximation in the superconducting phase.