  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.
