UC Davis

We explore the emergence of a variety of quantum phases of matter by performing computational studies of several model Hamiltonians. We begin by introducing the Holstein Hamiltonian which describes the electron-phonon interaction on a lattice, and present Determinant Quantum Monte Carlo (DQMC) simulations which reveal the subtle interplay between superconductivity and charge density wave order, focusing on the doped square lattice. We perform a finite-size scaling analysis of pair susceptibility data to accurately determine critical transition temperatures in this model. A recently developed Hybrid Monte Carlo (HMC) algorithm is used to explore charge ordering on the kagome lattice, where we discover a long-ranged charge ordered phase. We then discuss integer-spin Kitaev honeycomb models, and present numerical studies of their thermodynamic behavior. We illustrate the sensitivity of the quantum spin liquid phase to single-ion anisotropy, and discuss the rich variety of thermodynamic behavior in these models. The disordered Ising antiferromagnet on the triangular lattice is also analyzed using transfer matrix calculations and classical MonteCarlo techniques. Our focus here is on the robustness of residual entropy plateaus to disorder and other perturbations, and discuss the relevance of these results to experimental systems. Finally, we present a study of the triangular lattice Hubbard model in a magnetic field, focusing on large U/t at temperatures beyond the exchange parameter J = 4t^2/U. Motivated by recent experiments on triangular lattice compound LCSO, we compare our numerical results for magnetization and entropy to experimental data.