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

Fenner Harper; N. Read; Steven H. Simon

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

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arxiv 1402.1174 v1 pith:QYWSFPY5 submitted 2014-02-05 cond-mat.str-el cond-mat.mes-hall

Steven H. Simon , Fenner Harper , N. Read This is my paper · ORCID

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keywords conductivityformulahallelementarycannotchamonchernclaimed

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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 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.

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