  The experimental realization of the Harper-Hofstadter model in ultra-cold
atomic gases has placed fractional states of matter in these systems within
reach---a fractional Chern insulator state (FCI) is expected to emerge for
sufficiently strong interactions when half-filling the lowest band. The
experimental setups naturally allow to probe the dynamics of this topological
state, yet little is known about its out-of-equilibrium properties. We explore,
using density matrix renormalization group (DMRG) simulations, the response of
the FCI state to spatially localized perturbations. After confirming the static
properties of the phase we show that the characteristic, gapless features are
clearly visible in the edge dynamics. We find that a local edge perturbation in
this model propagates chirally independent of the perturbation strength. This
contrasts the behavior of single particle models with counter-propagating edge
states, such as the non-interacting Harper-Hofstadter model, where the
chirality is manifest only for weak perturbations. Additionally, our
simulations show that there is inevitable density leakage from the first row of
sites into the bulk, preventing a naive chiral Luttinger theory interpretation
of the dynamics.
