Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators

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. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. We further generalize our approach to the time-reversal invariant analog of fractional quantum Hall states--fractional topological insulators, and provide the first explicit wavefunction description of fractional topological insulators in the absence of spin conservation.