Wave functions for fractional Chern insulators

We provide a parton construction of wave functions and effective field theories for fractional Chern insulators. We also analyze a strong-coupling expansion in lattice gauge theory that enables us to reliably map the parton gauge theory onto a microscopic electron Hamiltonian. We show that this strong-coupling expansion is useful because of a special hierarchy of energy scales in fractional quantum Hall physics. Our procedure is illustrated using the Hofstadter model and then applied to bosons at half filling and fermions at one-third filling in a checkerboard lattice model recently studied numerically. Because our construction provides a more or less unique mapping from microscopic model to effective parton description, we obtain wave functions in the same phase as the observed fractional Chern insulators without tuning any continuous parameters.