Mixed magnetic order and superconductivity in multiorbital Hubbard models

We extend a generalized Hartree-Fock theory that allows mixed phases to multiorbital Hubbard models. Multiband and multiorbital physics are crucial for the understanding of superconductivity and magnetism and their possible coexistence in high-temperature superconductors. Handling that kind of system can be numerically expensive and is in general restricted to a limited number of ordering vectors in the standard Hartree-Fock approach. Applying a generalized Hartree-Fock theory including the minimization of the grand canonical potential allows to overcome these drawbacks and thereby permits extensive studies of phases of mixed magnetic order. Furthermore, we have enhanced the usual tetrahedron integration method by an adaptive refining algorithm at zero and finite temperatures. Using these methods, we are able to employ realistic multiorbital models to study the coexistence and competition of magnetic ordering or mixing and superconductivity. We elucidate the role played by orbital effects and compare with previous work J. Schmiedt et al., Phys. Rev. B 85, 214425 (2012). Furthermore, we study the possibility of additional phase transitions in the coexistence regime.