UC Davis

Topological materials are of great interest to condensed matter physicists and engi-neers alike due to their potential application in quantum technology. To this end, two materials in this class, Weyl semimetals and quantum spin liquids, are studied in this dissertation using a set of computational and theoretical techniques. Quantum spin ice models are studied using exact diagonalization, numerical linked cluster expansions, and perturbation theory. We calculate a host of observables like entanglement entropy and Ising correlation, and use them extract the phase bound- aries of these models as a function of model parameters. These results have potential application in the experimental study of rare-earth pyrochlores. We study the Hall transport properties of Weyl and multi-Weyl semimetals un- der the periodic drive of a laser pulse using analytical methods such as the Kubo formalism and the Matsubara Green's function formalism. Physical quantities such as the thermal Hall and Nernst conductivities are extracted for such models. The information obtained is analyzed and we show the characteristics of the transport coecients as a function of monopole charge. i