We respond to the comments expressed by L. D'Alessio in arXiv:1412.3481 on our work "Floquet Fractional Chern Insulators" [Phys. Rev. Lett. 112, 156801 (2014)]. We confirm the central result that the ground state of the effective Hamiltonian is an interacting fractional Chern insulator.
In a recent paper [Phys. Rev. Lett. 112 156801 (2014)], Grushin et al. studied a Fermi-Hubbard-model for spinful electrons on a honeycomb lattice coupled to an external polarized electric field. By computing the Floquet Hamiltonian perturbatively to order ω−1 (where ω is the frequency of the drive) they predicted that, for specific values of the driving and filling, the system can transition into a Fractional Chern Insulator. In this comment we point out that: i) the calculation of the Floquet Hamiltonian misses some terms of order ω−1 and ii) the assumption that the Floquet bands are filled as in time-independent systems is questionable.