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Center for Nonlinear Studies |
The study of topological states of matter is fundamental important to our knowledge of novel phases beyond the Landau paradigm. In recent years, there is the exciting prospect of realizing topological properties in strongly interacting systems, which may significantly extend the classes of topological states of matter. In this talk, I will introduce several different microscopic systems where electron correlation effects are of crucial importance. Examples include interaction-driven quantum anomalous Hall effect that features time-reversal symmetry spontaneously breaking, fractional quantum Hall effect at filling factor 12/5 with "fibonacci" quasiparticles, and fractional Chern insulator exhibiting anyonic statistics. In particular, I will show how to efficiently identify topological properties of a given ground state by implementing state-of-the-art density-matrix renormalization group and exact diagonalization simulations. These newly developed techniques pave an avenue towards diverse topics in strongly interacting topological phases.
Host: Jianxin Zhu