A quantum Monte Carlo method and its applications to multi-orbital Hubbard models

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multiorbital Hubbard models. Our formulation can he applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase. transitions such as metal-insulator. magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.