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 ${\sigma }_{xy}$ 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 that 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.

• Received 11 February 2014

DOI:https://doi.org/10.1103/PhysRevB.89.127101