Correlation Effect In Heavy Electron System

The heavy fermion/electron system is one of the most active and promising research ?elds in modern condensed matter physics, in which countless emergent phenomena appears like heavy Fermi liquid behavior, unconventional superconductivity, strange metal, quantum criticality and so on. However, due to the electron correlation effect which cannot be captured by conventional mean-?eld and perturbation theory, the theoretical study in this ?eld is slow and does not receive proper attention. But, we perceive that slave-particle-based mean-?eld approach and numerical techniques like quantum Monte Carlo and dynamic mean-?eld theory have changed this trend and it is our opportunity to immerse into this fruitful but largely unexplored ?eld. In this thesis, we have systematically studied electron correlation effect in heavy fermion systems in terms of model Hamiltonian, e.g. Kondo lattice and periodic Anderson lattice model, via both analytical and numerical techniques. Speci?cally, we have provided an alternative description of quantum criticality in terms of orbital-selective orthogonal metal transition, which is obtained by applying novel Z2slave-spin mean-?eld theory.The divergent speci?c heat and quasi-linear-T resistance is reproduced and is consistent with experiments. Next, turning on spin-orbit coupling, we have found topological antiferromagnetic spin-density-wave on Haldane-Kondo lattice model. The unique feature of such state is the non-trivial quantum Hall response to external electromagnetic ?eld, which is obviously beyond the framework of topological Kondo insulator. Then, we further explore possible topological properties in Kondo-necklace model with the help of quantum non-linear sigma model and appropriate topological term. It is found that Kondo-necklace model in two or three dimensions may support certain kinds of symmetry-protected topological states. Motivated by recent experiments in CeCoIn5, we have studied fermionology and unconventional superconductivity in Kondo-Heisenberg model, which gives rise to a uni?ed description of normal state Fermi surface and the origin of pairing instability. Finally, constraint path Monte Carlo method is explained in detail and applied to periodic Anderson model, where good agreement with previous works is shown. We hope the present work may be helpful for understanding the complex phenomena in heavy fermion materials.