Phase Diagram Of Kagome-Hubbard Model-Dynamical Mean Field Theory Study

As an important concept in condensed matter physics,strong correlation effect plays an important role.Different from the traditional solid-state physical system,in the strong correlation system,the electron-electron interaction becomes more and more important,and has a fundamental impact on the nature of the system.From the point of view of the electron-electron interaction,people have solved or partially solved many difficult problems in the physical field for a long time,such as Mott insulator,Kondo effect,high temperature superconductivity and magnetic origin,etc.However,due to the existence of electron-electron interaction,it is difficult for traditional research methods to further study the strong correlation system.Recently,due to the development of computer science and technology,people have put forward a lot of calculation methods to solve the strong correlation system based on numerical calculation,for example,random phase approximation(RPA),quantum Monte Carlo(QMC),variational Monte Carlo(VMC),dynamical mean field theory(DMFT),numerical renormalization group(NRG),renormalization group(RG),density matrix renormalization group(DMRG),functional renormalization group(FRG),etc.in this paper,we use the dynamical mean field theory to study the phase diagram of the single band Kagome-Hubbard model in strong correlated systems.The paper is divided into the following parts.First of all,I will introduce the development of the study of strong correlation effect,including various physical phenomena involved in strong correlation effect,the representative model of strong correlation system-Hubbard model,is introduced in detail.In the study of strong correlation effect,the mechanism of high temperature superconductivity and the origin of magnetism are the most concerned.In the traditional BCS superconductivity theory,electrons and electrons form Cooper pairs with lower energy under electron-phonon coupling,and the pairing symmetry is the traditional S-wave.In combination with the GL equation,the origin of superconductivity and various physical properties of traditional superconductivity can be systematically explained,including Meissner effect,specific heat jump,single particle tunneling effect,Josephson effect and so on.However,many high-temperature superconductors discovered later have different properties from traditional superconductors,such as superconducting transition temperature beyond Mc Millan limit,unique single particle tunneling spectrum,unconventional pairing symmetry and so on.In this kind of materials,electron-electron interaction plays an important role,the Hubbard model and its derived t-J model describe the characteristics of high-temperature superconducting materials perfectly.In magnetic materials,the electron electron interaction also plays a key role in many magnetic processes,they can also be described using the Hubbard model and its derivatives.The typical representative is the stoner criterion for Hubbard model with outfield under mean field approximation,the Kondo effect caused by the introduction of magnetic impurities,and the indirect exchange between the local magnetic moments transmitted by conduction electrons,i.e.RKKY interaction.Finally,I will introduce the motivation of the study.Next,I will introduce the basic idea of the dynamical mean field theory,including the approximation of Hubbard model in high dimension,the transition scheme from Hubbard model to Anderson model,the implementation and derivation process of self consistent scheme,and the treatment of ordered phases.By using the dynamical mean field theory,we can simplify the hard to solve Hubbard model into a single channel Anderson model that can already be solved numerically,so as to realize the solution of the single band Hubbard model on the Kagome lattice,and get the change of magnetic order with U at low temperature.Then,I will introduce how to solve the simplified single channel Anderson model.At present,there are many methods that can be used to solve the Anderson model,such as exact diagonalization,quantum Monte Carlo,numerical renormalization group method,etc.I will focus on the numerical renormalization group method.Based on the above theory,we calculate the average magnetic moment at zero temperature.The results are compared with the results of the random phase approximation method of the collaborators and the Predecessors' results.The results show that the system will indeed undergo a ferromagnetic to 120 degree antiferromagnetic phase transition.Combined with the study of the variational Monte Carlo method of the following partners,we have obtained the specific magnetic phase diagram of the Kagome-Hubbard model under the van Hove occupation with U.Finally,we summarize and prospect the relevant results and areas.