Schwinger Boson Approach For Dynamical Mean-field Theory

The strongly correlated electron system is an important part of condensed matter physics,where the many-body interaction energies dominate the kinetic energies.As a result,the interaction is large enough to qualitatively modify the macroscopic properties.On the one hand,various exotic physical phenomena emerge in the strongly correlated electron systems,such as the Mott metal-insulator transition,the high-temperature superconductivity,and so on.On the other hand,it is difficult to describe these systems via traditional perturbation theory due to the strong interaction among electrons.For the above two reasons,strongly correlated electron systems have attracted continuous attention.Heavy-fermion systems are typical strongly correlated electron systems.In heavyfermion compounds,collective hybridization develops between local 1)electrons and itinerant conduction electrons,which gives rise to electron quasiparticles with effective masses in excess of hundreds or thousands of the bare-electron mass.Besides,various exotic phenomena have been observed in heavy-fermion materials,such as the localitinerant transition of 1)electrons,unconventional superconductivity,and non-Fermiliquid behaviors.Many theoretical and numerical approaches have been adopted to investigate the microscopic mechanisms underlying these phenomena.The dynamical mean-field theory(DMFT)provides a simple yet powerful way to study heavy-fermion physics.In the framework of DMFT,a lattice model is mapped to an effective single-impurity model.Then the impurity model can be solved by impurity solvers,such as the non-crossing approximation,the continuous-time quantum Monte Carlo method,the numerical renormalization group,and so on.Each of them has its own pros and cons.Therefore,improving the performance of impurity solvers or developing new impurity solvers is one of the most important frontier research topics in the development of DMFT.Motivated by the success of the large- Schwinger boson approach in the heavyfermion systems,we take the Schwinger boson technique as an impurity solver for DMFT calculations of the Kondo lattice model in this thesis.The resulting thermodynamic and transport properties are in qualitative agreement with more rigorous calculations.Meanwhile,compared to the earlier slave boson mean-field approach,our method further clarifies the crossover behavior in a wide range of temperature,from the local moment regime to the Fermi liquid regime.Due to its wide applicability and high computational efficiency,our method has the potential to be extended and combined with other methods,such as the density functional theory for efficient material calculations.Compared with the single-band models,multi-orbital models are more realistic involving the spin-orbital coupling,the crystal field effect and the Hund’s coupling.Based on the Schwinger boson approach,we further design an impurity solver for solving a general multi-orbital Anderson model.At present,we have completed the program testing and are exploring the microscopic mechanisms of this method.