FERMION SIMULATIONS OF CORRELATED SYSTEMS

Recently developed simulation algorithms for strongly correlated lattice fermions are reviewed. The simulation methods which we describe are based on the path-integral formalism. Basic algorithms for auxiliary-field methods as well as prescriptions for reducing the minus-sign problem are presented. As an important application, ground state properties of the Hubbard model are discussed in the light of recent simulation results. Clarified so far, important features of antiferromagnetic transitions, metal-insulator transitions and pairing mechanisms in strongly correlated systems are summarized. Recent applications of the fermion Monte Carlo method to other fermion models with degenerate orbitals such as the d-p model are also reviewed. Heavy fermion systems, exhibiting a variety of crossovers such as the temperature crossover between the intersite antiferromagnetic correlation and the local singlet formation, are also discussed. Pairing mechanisms examined numerically in a variety of extended lattice models are briefly sketched.