Monte Carlo Simulations Of Frustrated Quantum Spin Systems On The Pyrochlore Lattice

Frustrated quantum spin systems have plenty of exotic properties with the effects of geometrical frustration and quantum fluctuations.At very low temperature,quantum spin liquids(QSLs)will emerge.From the perspective of magnetic order,QSLs have no peaks in the whole Brillouin zone in the thermodynamical limit.It is magnetic dis-order.But in this "disorder" world,topological excitation,gauge structure and so on will emerge.Quantum spin ice(QSI)is an important member of this family.Due to the similarity to one structure of water ice,it is called as quantum spin "ice".At present,the knowledge of QSI is more than other type of QSLs.But there are still many questions about QSI by cause of its strongly correlations and they attract us to dig out.In this thesis,we will employ unbiased quantum Monte Carlo(QMC)calculations to simulate static and dynamic properties of QSI.There are fundamental differences of topological excitations in QSI from those of the conventional magnets.The direct detecting approach of these topological excita-tions is to measure spectra.Using large-scale QMC simulations and stochastic analytic continuation(SAC),we first observe signatures of coherent photon and spinon excita-tions in the dynamic spin structure factor.In the QSI region,the large half width indicate the significant decay of photon.Comparing the results of QMC-SAC results with the analytical calculations,the numerical spectra suggest the spinon behaves as a coherent quasipartical with renormalized hopping amplitude.With the temperature increasing to the classical spin ice region,the photon disappears but there is still a dispersive spinon continuum.As the temperature further increases,all effects causing by quantum fluctua-tions fade.Spectra can also be used as judgments of the existence of QSI in experiments and our results provide experimentally relevant,quantitative information for the pursuit of QSI materials.XYZ model on a pyrochlore lattice is a real model in real quantum magnetic ma-terials and it is an important model in both theories and experiments.Combined with gauge mean-field theory and QMC calculations,we determine the phase diagram of this model in a large parameter regime.We find that the U(1)Coulomb liquid(QSI)is quite stable and spans a rather large portion of phase diagram with pairing term.Moreover,we numerically find that weak pairing term could induce a possible Z2 spin liquid in a small region before the system entering the order phase.But to resolve it,more detailed investigations are needed.