Condensed Matter Physics Seminar

We propose a systematical approach to construct generic fractional quantum anomalous Hall (FQAH) states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. New states that are absent in the ordinary fractional quantum Hall system are also proposed. We further generalize our approach to time-reversal invariant fractional topological insulators.