Electronic Nematic Phase And Quantum Spin Liquid Of The Strongly-correlated System

Strongly correlated electronic systems attract great attention for their unique and complex quantum phenomena,rich phase diagrams,and potentially widespread applications,and have been at the forefront of condensed matter physics research for nearly three to four decades.Particularly interesting in recent years are the existence of two peculiar types of magnetic phases,electron nematic phases and quantum spin liquids(QSL),which are long-range disordered but have static and dynamic short-range magnetic orders,respectively.In order to understand the physical mechanisms behind these anomalous phenomena,in this dissertation,we studied the microscopic mechanisms of these two phenomena using a variety of theoretical methods suitable for dealing with strong correlation systems.We first used the variational Monte Carlo(VMC),finite temperature Lanczos(FTLM)and Schwinger boson mean field(SBMF)methods to study the electron phases of the two-dimensional and three-dimensional In3Cu2VO9 hexagonal lattice systems within the single-band Hubbard and Heisenberg models,respectively.We show that the ground state of this system may be a general spin disordered phase,rather than electronic nematic one.Subsequently,we studied the ground-state evolution and quantum phase transition of the anisotropic Kitaev model under the magnetic field using FTLM and Majorana fermion mean field methods,respectively,and found that the competition between the anisotropic Kitaev coupling and the magnetic field leads to a richer phase diagram than the isotropic situation.Next,we designed a superconductor-monolayer Kitaev QSL-superconductor tunneling junction and explored the Majorana fermion kinetics or energy spectroscopic characteristics of the anisotropic Kitaev model by the transport properties of its current and conductance.In the s-d exchange model,we found that the single-particle conductance can well reflect the dynamic spin correlation characteristics of Kitaev QSL.In the Anderson lattice model,we found that the superconducting current characteristics at zero magnetic field are clearly distinguished the ferromagnetic from the antiferromagnetic situations,which are the evidence of the existence of Kitaev QSL.The dissertation is arranged as follows:In the first chapter we introduce the characteristics of strongly correlated systems and their related models,including the Hubbard models,spin models,s-d exchange models,and Anderson lattice models,respectively.Then we describe the concept,origin and properties of electronic nematic phase,their presence in iron-and copper-based high-temperature superconductors,and their possible presence in In3Cu2VO9.Finally,the concept,origin and properties of QSL,the precise solution and spin correlation of the Kitaev model,the Kitaev material,and the recent research results of the Kitaev model under the magnetic field are introduced.In the second chapter we mainly introduce the three methods used in this dissertation,namely variational Monte Carlo,finite temperature Lanczos,and non-equilibrium Grimm functions methods,including their background,method principles,and practical applications.We in the third chapter first explore the electronic nematic phase of the twodimensional hexagonal lattice system In3Cu2VO9 under the VMC method in the singleband Hubbard model,and then studies the electronic nematic phase of the threedimensional In3Cu2VO9 using the finite temperature Lanczos and Schwinger boson mean field methods in the single-band J1-J2-Jc Heisenberg model.The results show that the in-plane and interlayer spin couplings frustrations,as well as the magnetocrystalline anisotropy,as "spin drivers",are difficult to lead to the emergence of electronic nematic phase,which proves that the three-dimensional In3Cu2VO9 ground state may be a general spin disordered phase.In the fourth chapter we adopt the Majorana fermion mean field method and the finite temperature Lanczos method to study the topologically quantum phase transition characteristics of the anisotropic Kitaev model under the magnetic field.We found that there are one or two new topological or trivial quantum phase transitions,in comparison with the isotropic Kitaev model.At these critical points,the low-energy excitation spectrums appear level crossover,and the specific heat,magnetic susceptibility and Wilson ratio display anomalies;accordingly,the topological Chern number may also change.Therefore,the magnetic field can be used to modulate the QSL states with different topologies to realize the design of quantum calculation devices in real materials.In the fifth chapter we study the dynamical spin correlations of the Kitaev QSL and the characteristics of single-particle energy spectroscopy by using the transport of the superconductor-monolayer Kitaev QSL-superconductor junction in the s-d exchange model and the Anderson lattice model,respectively.In the s-d exchange model,we found that the single-particle conductances well reflect the dynamical spin correlation characteristics of Kitaev QSL,including unique spin gap,damping associated with th van Hove singularities,and spinon-vison interaction peaks,and different topological quantum phases of QSL can be distinguished according to their spectral characteristics.In the Anderson lattice model,we found that at zero magnetic field,the superconducting current will have two tunneling resonant peaks,corresponding to the localized and itinerant Majorana fermion modes of QSL,respectively.The increase in magnetic field inhibits their energy spectral density,causing the current to gradually decrease until it enters the polarized ferromagnetic phase and reaches a platform.These features can distinctly distinguish the ferromagnetic from the antiferromagnetic situations and are the evidence of the existence of Kitaev QSL.In the sixth chapter we summarize the results of this paper,summarizes the core innovation,and finally gives some prospects for future research.