Feng, Kexin2022-04-132022-04-132022-01https://hdl.handle.net/11299/226935University of Minnesota Ph.D. dissertation. 2022. Major: Physics. Advisor: Natalia Perkins. 1 computer file (PDF); 193 pages.Quantum spin liquids (QSL) is a novel state of magnetic material, where magnetic order is absent down to very low temperature. This novel state has massive quantum entanglement, and can host emergent quasiparticle excitations, which carry fractionalized quantum numbers and display anionic statistics. In this thesis, I focus on the phonon and thermal dynamics of the Kitaev QSL, explore detectable signatures of QSL phase. More specifically, I will new propose observables, including sound attenuation coefficient, Hall viscosity and Fano effects in the optical phonon Raman spectroscopy, which are shown to encode information of the fractionalized excitations, namely Z2 gauge fluxes and itinerant fermions. The key technique to deal with spin-phonon couplings largely relies on symmetry considerations, which involves group and representation theory. The main numerical technique to simulate flux thermodynamics are Markov Chain Monte Carlo and stratified Monte Carlo. The latter is a new efficient algorithm which I designed specifically for the Kitaev model, based on my phenomenological study of the Z2 flux thermodynamics.enFractionalized excitationsMonte CarloQuantum Spin LiquidsSpin phonon couplingSymmetryThesis or Dissertation