Numerical simulation of quantum many-body systems

Understanding the physical properties of strongly interacting many-electron systems remains one of the central goals of condensed matter physics. In this project, the authors have developed and implemented numerical techniques, such as quantum Monte Carlo simulations, to study basic models of interacting electrons: the one-band Hubbard model for positive and negative U, the three-band CuO2 Hubbard model, the Holstein electron-phonon model, the periodic Anderson model, and the Kondo lattice. Such models exhibit a rich variety of physical properties. For example, the half-filled Holstein model undergoes a Peierls-charge-density wave transition. While away from half-filling there is competition between superconductivity and the Peierls-charge-density wave phase. The ground state of the half-filled 2D Hubbard model has long-range antiferromagnetic order. Away from half-filling, it has been found to have an attractive interaction in the singlet dx2-y2 pairing channel, and it provides a model for the high-temperature cuprate superconductors. Similarly, it is believed that the periodic Anderson model and the Kondo lattice model provide a framework for understanding the heavy fermion materials which can exhibit antiferromagnetic and superconducting phases. Because of the strong coupling and the interplay between the different correlations, it is possible to tip these delicately balanced systems in favor of a given correlated state by the approximations one makes. Thus it is important to develop systematic, controlled calculations for these models. Numerical calculations provide an important approach for determining the properties of such models. A review of the work on these problems is presented