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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 Hallconductivity of fractional Chern insulators. We show that the proposed formulacannot generally be correct, and we suggest one possible source of the error.Our reasoning can be generalized to show no quantity (such as Hallconductivity) expected to be constant throughout an entire phase of matter canpossibly be given as the expectation of any time independent short rangedoperator.

Comment on "Elementary formula for the Hall conductivity of interacting systems"