Theoretical Investigations On The Quantum Phases And Spin Dynamics Of Spin-orbital Systems

The emergence of spin-orbital Mott insulators promotes the researches on the mul-tipolars and spin liquids.Due to the entanglement of the spin and orbital,the ground states of transition-metal oxides are suggested to be unconventional magnetism,includ-ing spin liquids,multipolar orders and uncommon magnetic orders.The system with high degrees of freedom,such as the high spin and spin-orbital system,can be regarded as special cases of SU(N)spin systems.Thus it is important to study SU(N)spin sys-tems.Here we intend to introduce the SU(N)spin-wave theory and parafermion parton representation for the studies of SU(N)spin systems:1.We present the application of the SU(N)spin-wave theory to spin-orbital Mott insulators whose ground states exhibit magnetic orders.If we take both degrees of free-dom of spin and orbital into account rather than projecting onto the Kramers doublet,which is the lowest energy spin-orbital locking levels of the spin orbital coupling,the SU(N)spin-wave theory is suggested instead of the SU(2)spin-wave theory due to the inevitable spin-orbital multipole exchange interactions.To coordinate with the SU(N)linear spin-wave theory,we introduce an efficient general local mean field approach which involves all the local fluctuations and illustrate the advantages of the SU(N)linear spin-wave theory by presenting a multipolar spin-wave spectra of the SU(4)an-tiferromagnetic model.Then we apply it to spin-orbital Mott insulators.It is revealed that the Hund's coupling would influence the effectiveness of the isospin-1/2 represen-tation when the spin orbital coupling is not large enough.Besides,we also attempt to do a preliminary simulation based on the first principle calculations for concrete ma-terials,?-RuCl3 and Sr2IrO4.The SU(N)spin-wave theory appropriately depicts the low-energy magnons and the spin-orbital excitations qualitatively.In addition,we also demonstrate the continuum of the spectra of YbZnGa04 results from the disorders by the SU(N)spin-wave theory.2.To study the exotic excitations described by parafermions in the possible liquid states of SU(n)spin system,we introduce a parafermion parton approach.The SU(n)spin operators can be written as the clock and shift matrices,which are shown to be the polynomials of parafermion operators in the parafermion representation.We find that SU(n)spins can be decomposed into the n parafermion matrices of degree one.In this decomposition,the spin has a {(?)SU(n)}n-1 gauge symmetry.As an application,we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory,both of them have been proved to be related to parafermion excita-tions.We find that with the symmetries of translations,6-fold rotation and combination of parity and time reversal,there are 9 types and 102 solutions for two-dimensional Z3 parafermion spin liquids on the honeycomb lattice.On the contrast,there will be 9 types and 36 solutions if both parity and time-reversal symmetries are present.Our results provide a novel route for the systematic search of the new types of spin liquids with exotic any on excitations.