MICROSCOPIC DERIVATION OF THE SO(5) SYMMETRICAL LANDAU-GINZBURG POTENTIAL

We construct a microscopic model of electron interactions that gives r ise to both superconductivity and antiferromagnetism, and which admits an approximate SO(5) symmetry that relates these two phases. The symm etry can be exact, or it may exist only in the long-wavelength limit, depending on the detailed form of the interactions. We compute the mac roscopic Landau-Ginzburg free energy for this model as a function of t emperature and doping, by explicitly integrating out the fermions. We find that the resulting phase diagram can resemble that observed for t he cuprates, with the antiferromagnetism realized as a spin-density wa ve, whose wavelength might be incommensurate with the lattice spacing away from half filling.