Composite Fermions for Fractionally Filled Chern Bands

A band with a nontrivial topology, as characterized by a nonzero Chern number, is called a Chern band. When such a band is filled, it displays a quantized integer Hall conductance. Recent numerics show that when such a band is partially full and the electrons in it are subject to strong repulsive interactions, ground states reminiscent of fractional quantum Hall states are found at particular fractional filling. I will show that this is not an accident by constructing an algebraically exact mapping from such bands to fractional quantum Hall problems in terms of operator-based Composite Fermions. On the lattice, one can realize not only the usual FQH states of the continuum, but also states whose existence depends on the lattice, and whose filling can be different from the Hall conductance.