Variational ground state of a two-orbital Hubbard model

An optimization variational Monte Carlo method is formulated for a two-dimensional Hubbard model with doubly degenerate atomic orbitals. We use generalized Gutzwiller-type wave functions, which include all the possible intra-atomic correlations. As a demonstration, we show results of energy and some correlation functions for a special case; at a quarter filling and for large Coulomb interactions, a ferromagnetic state with an orbital order overcomes paramagnetic and superconducting states. However, this ferromagnetism is destabilized by electron doping or by introducing a diagonal transfer in one direction, both of which work as substantial frustrations.