Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect

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Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect

Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, and Eduardo Fradkin

Phys. Rev. Lett. 114, 016805 – Published 7 January 2015; Erratum Phys. Rev. Lett. 114, 149902 (2015)

Abstract

We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.

Received 9 November 2014

DOI:https://doi.org/10.1103/PhysRevLett.114.016805

Erratum

Erratum: Framing Anomaly in the Effective Theory of the Fractional Quantum Hall Effect [Phys. Rev. Lett. 114, 016805 (2015)]

Andrey Gromov, Gil Young Cho, Yizhi You, Alexander G. Abanov, and Eduardo Fradkin

Phys. Rev. Lett. 114, 149902 (2015)

Authors & Affiliations

Andrey Gromov¹, Gil Young Cho², Yizhi You², Alexander G. Abanov^1,3, and Eduardo Fradkin^2,4

¹Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA
²Department of Physics and Institute for Condensed Matter Theory, University of Illinois, 1110 W. Green St., Urbana, Illinois 61801-3080, USA
³Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York 11794, USA
⁴Kavli Institute for Theoretical Physics, University of California Santa Barbara, California 93106-4030, USA