Bimetric Theory of Fractional Quantum Hall States
Abstract
We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist of a topological Chern-Simons action, coupled to a symmetric rank two tensor, and an action à la bimetric gravity, describing the gapped dynamics of the spin-2 GMP mode. The theory is formulated in curved ambient space and is spatially covariant, which allows to restrict the form of the effective action and the values of phenomenological coefficients. Using the bimetric theory we calculate the projected static structure factor up to the k6 order in the momentum expansion. To provide further support for the theory, we derive the long wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. Finally, it is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Chicago, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1408269
- Alternate Identifier(s):
- OSTI ID: 1499001; OSTI ID: 1595671
- Grant/Contract Number:
- FG02-13ER41958; SC0009924
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. X
- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2160-3308
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Gromov, Andrey, and Son, Dam Thanh. Bimetric Theory of Fractional Quantum Hall States. United States: N. p., 2017.
Web. doi:10.1103/PhysRevX.7.041032.
Gromov, Andrey, & Son, Dam Thanh. Bimetric Theory of Fractional Quantum Hall States. United States. https://doi.org/10.1103/PhysRevX.7.041032
Gromov, Andrey, and Son, Dam Thanh. Fri .
"Bimetric Theory of Fractional Quantum Hall States". United States. https://doi.org/10.1103/PhysRevX.7.041032.
@article{osti_1408269,
title = {Bimetric Theory of Fractional Quantum Hall States},
author = {Gromov, Andrey and Son, Dam Thanh},
abstractNote = {We present a bimetric low-energy effective theory of fractional quantum Hall (FQH) states that describes the topological properties and a gapped collective excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist of a topological Chern-Simons action, coupled to a symmetric rank two tensor, and an action à la bimetric gravity, describing the gapped dynamics of the spin-2 GMP mode. The theory is formulated in curved ambient space and is spatially covariant, which allows to restrict the form of the effective action and the values of phenomenological coefficients. Using the bimetric theory we calculate the projected static structure factor up to the k6 order in the momentum expansion. To provide further support for the theory, we derive the long wave limit of the GMP algebra, the dispersion relation of the GMP mode, and the Hall viscosity of FQH states. We also comment on the possible applications to fractional Chern insulators, where closely related structures arise. Finally, it is shown that the familiar FQH observables acquire a curious geometric interpretation within the bimetric formalism.},
doi = {10.1103/PhysRevX.7.041032},
journal = {Physical Review. X},
number = 4,
volume = 7,
place = {United States},
year = {Fri Nov 10 00:00:00 EST 2017},
month = {Fri Nov 10 00:00:00 EST 2017}
}
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https://doi.org/10.1103/PhysRevX.7.041032
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