Numerical Study Of Low-dimensional Magnetic Systems

Many years ago,people discovered spontaneous macro magnetism of matter in the colorful nature.Spontaneous magnetic orders originate from the interaction and correlated effects between electrons in the magnetic materials.Therefore,magnetism is closely related to some other novel phenomena resulting from correlated many-body effects.For example,after destabilizing antiferromagnetic order in some Mott insulators by doping or pressurizing,unconventional superconductivity may arise,and the antiferromagnetic fluctuations are considered to play an important role in the appearance of superconductivity.In addition,the magnetic systems themselves own many interesting phenomena.For low-dimensional magnetic systems,limited spatial dimension and frustration will lead to strong quantum effects.Consequently,novel states and excitations may emerge in low-dimensional magnetic systems.For instance,symmetry protected topological phases and Tomonaga-Luttinger liquids in one-and quasi-one-dimensional systems,quantum spin liquid states and fractional excitations in highly frustrated systems.With strong quantum fluctuations,novel quantum phase transitions and quantum criticality,such as deconfined quantum phase transition,may happen in magnetic systems.Because of the close connection between magnetism and the other many-body phenomena,as well as the novel physical phenomena in the magnetic systems itself,the study of quantum magnetism is one of the important areas in strongly correlated electron systems.To understand the strange phenomena in magnetic systems,a lot of theoretical models have been proposed.Unfortunately,due to strong quantum fluctuations and correlated effects,especially in two dimensions,existing analytical methods break down.On the other hand,with the renewal of computer hardware,it is possible to do large-scale numerical simulations nowadays.Therefore,many-body numerical methods play a crucial role in both establishing the picture of theoretical models and understanding the properties of magnetic materials.The densitymatrix renormalization group(DMRG)is one of the important numerical methods,which is widely used in the explorations of quantum magnetism.In this thesis,we will introduce some research results about two kinds of low-dimensional magnetic systems by using DMRG simulations,one is one-dimensional spin cluster-based system,and the other is Kitaev material with high spin,we will discuss in the following,respectively.Recently,experimental results show that we can realize the symmetry protected S=1 odd Haldane phase in edge-shared tetrahedral chains,and theoretical analyses show that the odd Haldane phase occurs when the number of tetrahedron np in a cluster is an arbitrary even number.In reality,there are also onedimensional cluster materials with a single tetrahedron in a cluster.These results naturally bring us the following questions—what are the differences and relationships in the materials with different parity of np?And for arbitrary odd nps,is there an odd Haldane phase?More generally,what other phases may appear in edgeshared tetrahedral materials in one dimension?Motivated by the crystal structure of the edge-shared tetrahedral materials,we construct two-leg ladder models of edge-shared tetrahedral spin clusters.Their ground phase diagrams are obtained by DMRG simulations,the numerical results show that the phase diagrams strongly depend on the parity of np.For even np,there are two phases,one is the odd Haldane phase,and the other is a cluster rung-single phase.However,for odd np,besides the two phases in the even np case,there are an even Haldane phase and a cluster-singlet phase.Moreover,in the odd np case,the region of the odd Haldane phase increases while that of the cluster-singlet phase and the even Haldane phase shrinks as np increases.By analyzing the origin of the odd Haldane phase in the two np cases,we conjecture that the parity effects will disappear in the large np limit,which is supported by our numerical results.Hunting for quantum spin liquid in frustrated spin systems attracts a lot of attention both in theories and in experiments.The spin-orbital coupled Mott insulators,containing Kitaev coupling,offer us a promising route to realize quantum spin liquid state,it is of great interest for people searching quantum spin liquid in Kitaev magnets.It is reported that Kitaev interaction may play a key role in stabilizing ferromagnetic order at finite temperature in Cr-based van der Waals materials,such as CrSiTe3,etc.The magnetic properties of these materials may be theoretically described by the JK??' model with single-ion anisotropy.Especially,a recent work pointed that quantum spin liquid may occur in CrSiTe3 with proper compression strain.However,the conclusion is drawn from the thermodynamic results of a 12-site cluster,so the finite-size effects are avoidable.Therefore,the quantum spin liquid is needed to be identified by numerical results on larger lattice sizes.Based on theoretical magnetic parameters of CrSiTe3,we calculate the ground state phase diagram of S=3/2 JK??' model about Heisenberg interaction by DMRG.When the Heisenberg interaction changed from ferromagnetic to antiferromagnetic,three ordered phases are found,and they are a ferromagnetic phase,a 120° phase and an antiferromagnetic phase.In our numerical results,no positive evidence is found to support the quantum spin liquid phase reported in the previous work,and we also discuss possible reasons for the disagreement.The magnetic models we investigated are tightly related to real materials.We believe that our results will promote subsequent theoretical and experimental investigations.