A mean field approach to the colored Hubbard model

By subdividing a 2d square lattice into plaquettes containing 4 lattice sit es each, the Hubbard Hamiltonian is reformulated in terms of different "col ored" fermion species. This makes it possible to describe e.g. antiferromag netic order or d-wave superconductivity in terms of expectation values of c omposite scalar fields. A suitable mean field approximation indeed reproduc es qualitatively the measured phase diagram and shows a competition between phases with antiferromagnetic ordering and d(x2-y2)-superconductivity at l ow temperatures.