Application Of Slave-Particle Method In Strongly Correlated Electron Systems

Strongly correlated electron systems have always been one of the most important branches of condensed matter physics.The interaction between electrons in strongly correlated electron systems will make them form strong quantum correlations,resulting in various novel quantum states,such as heavy fermion states,unconventional superconducting states,non-Fermi-liquid states,quantum spin liquid states,etc.Electron correlations controlled by non-thermodynamic parameters can also drive quantum phase transitions.In the first chapter of this thesis,we give a brief overview of this field and introduce two important models commonly used in theoretical research on strongly correlated electron systems,namely the Hubbard model and the Anderson lattice model.Because the Coulomb interaction in strongly correlated electron systems cannot be treated with perturbation,the traditional band theory and Landau Fermi-liquid theory are no longer applicable,requiring new methods to analyze the ground state properties of the systems and obtain the correct physical images.The Slave-Particle method is one of the most effective theoretical methods to deal with strongly correlated electron systems.This thesis adopts Slave-Particle method for research.In the second chapter of the thesis,we introduce two methods,one is the slave-boson method for dealing with Coulomb interaction when it tends to infinity,and the other is the slave-rotor method for representing the fermion operator as the product of the charge part and the spin part.The third chapter of this thesis is about our work on implementing half-semimetal in heavy fermion systems.The interest in the study of the semimetal family stems from the discovery of free-standing graphene.Meanwhile,the half-metal family with potential applications in quantum devices also attracts people to continuously carry out more in-depth research.In order to search for so-called half-semimetal state satisfying both features of the semimetal and half-metal in strongly correlated electron systems,we studied the Anderson lattice model defined on honeycomb lattice structure,which also includes ferromagnetic coupling of localized electron spins.Using the slave-boson method,we obtain a phase diagram showing the first-order phase transition from a decoupled local ferromagnetic phase to the heavy fermion ferromagnetic phase and paramagnetic phase.There are two different magnetic states in the magnetic heavy fermion phase: a ground state with small spin magnetization and a metastable state with large spin magnetization.When the total electron filling is fixed at 3/8,the system exhibits an ideal half-semimetal state protected by electron correlations.The fourth chapter of this thesis is about our work on exploring the spin liquid phase in the Kondo frustration system.The study of quantum spin liquids arose from the discovery of high-temperature superconductors.Geometric frustration is one of the important factors for the appearance of spin liquid phase in strongly correlated electron systems.However,due to the finite density of states on the Fermi surface,the local electrons and conduction electrons always undergo Kondo coupling in the heavy fermion system on triangular lattice,and the spin of the local electrons cannot form a spin liquid state decoupled from the conduction electrons.We study the AndersonHeisenberg lattice model defined on triangular lattice structure.This model includes not only the hybridization of conduction electrons and local electrons at the same lattice site,but also the hybridization between the nearest neighbors.Using the slave-rotor method,we find that the system has a finite hybridization strength,and when the hybridization strength is lower than this value,the local moment spin liquid phase emerges.In the fifth chapter of the thesis,we summarize the work that has been done and look forward to the research on strongly correlated electron systems.