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

Abstract

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.

6 pages plus 13 pages supplement

References in corpus (6)

• Exponential localization of Wannier functions in insulators
• Emergent Many-Body Translational Symmetries of Abelian and Non-Abelian Fractionally Filled Topological Insulators
• The insulator/Chern-insulator transition in the Haldane model
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Enhancing the stability of a fractional Chern insulator against competing phases
• Elementary formula for the Hall conductivity of interacting systems

Cited by in corpus (3)

• Topological Lattice Models with Constant Berry Curvature
• Fractional Chern Insulators in Bands with Zero Berry Curvature
• Erratum for "Elementary formula for the Hall conductivity of interacting systems"