Framing anomaly in the effective theory of the fractional quantum Hall effect

Andrey Gromov; Gil Young Cho; Yizhi You; Alexander G Abanov; Eduardo Fradkin

doi:10.1103/PhysRevLett.114.016805

Framing anomaly in the effective theory of the fractional quantum Hall effect

Phys Rev Lett. 2015 Jan 9;114(1):016805. doi: 10.1103/PhysRevLett.114.016805. Epub 2015 Jan 7.

Authors

Andrey Gromov¹, Gil Young Cho², Yizhi You², Alexander G Abanov³, Eduardo Fradkin⁴

Affiliations

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

PMID: 25615495
DOI: 10.1103/PhysRevLett.114.016805

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.