The Study Of Transition,Thermodynamic Measuerment And Dynamical Behavior In Quantum Magnet

Quantum phases and quantum phase transitions are important topics in quantum many body and condensed matter physics,as they are often the birthplace of new theo-ries and discoveries.For example,the study of transition metal oxides led to the finding of Mott insulator and Hubbard model and it's representative ofhigh-temperature su-perconductivity,the study of the antiferromagnetic Heisenberg ground state led to the resonance valence bond state(RVB)and quantum spin liquid(QSL).However,in com-plex quantum many-body systems,it is very difficult to obtain accurately solutions due to the exponential wall problem.Therefore,people try to find answer from the efficient quantum numerical methods.Among those methods,stochastic series expansion(SSE)method,as a quantum Monte Carlo(QMC)method,is commonly used in quantum spin system.By performing numerically simulation of the model based on SSE method,we can effectively obtain static physical quantities such as energy and specific heat,and combining with stochastic analytical continuation(SAC)method we can obtain dynamic information such as excitation spectrum.The research works in this thesis is comprised of three parts.Firstly,employing SSE combined with SAC,we investigate the extended XXZ model on the kagome lattice,and find out thatS^ZS^ZandS⁺S^-dynamical spin structure factor can reveal the anyonic spinon and vison excitations.In particular the translational symmetry fractionalization of the latter,leads to the continuum having an enhanced periodicity,which can help distinguish QSLs in spectroscopic techniques such as inelastic neutron or resonance(inelastic)X-ray scatterings.Then we study a 3D checkerboard J-Q model and compute the phase diagram of the model spanned by the axes of temperature,intra-and inter-plane interactions.As a sign-free model,it can re-alize plaquette singlet(PS)phase,the antiferromagnetic(AFM)ordered phase,and the transition between them,which all are components of phase diagram on sign-problem Shastry Sutherland(SS)model.Lastly,SrCu₂(BO₃)₂is such a material whose magnetic properties are well described by SS model.Along with heat capacity measurements in expeiment,we get a complete phase diagram and find the PS-AFM is a first order phase transition.Applying analysis of finite scaling and symmetry,we reveal the na-ture around multicritical point.With weak inter-layer interactions,which is close to 2D limit,there is a sign for emergent symmetry on first order phase transition.However,as the inter-layer interactions getting stronger,3D effects dominate and a conventional first order phase transition shows.