  In a recent paper by Neupert, Santos, Chamon, and Mudry [Phys. Rev. B 86,
165133 (2012)] it is claimed that there is an elementary formula for the Hall
conductivity of fractional Chern insulators. We show that the proposed formula
cannot generally be correct, and we suggest one possible source of the error.
Our reasoning can be generalized to show no quantity (such as Hall
conductivity) expected to be constant throughout an entire phase of matter can
possibly be given as the expectation of any time independent short ranged
operator.
