Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Golkar, Siavash; Nguyen, Dung X.; Son, Dam T.

doi:10.1007/JHEP01(2016)021

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Journal Article · Mon Jan 04 23:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP01(2016)021· OSTI ID:1327326

Golkar, Siavash ^[1]; Nguyen, Dung X. ^[2]; Son, Dam T. ^[2]

Univ. of Chicago, Chicago, IL (United States); University of Chicago
Univ. of Chicago, Chicago, IL (United States)

Here, we consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ_T(ω) and $$\bar{p}$$_T(ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q⁴ coefficient of the static structure factor S₄, and the high-frequency shear modulus of the ground state μ_∞, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S₄ is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Chicago, Chicago, IL (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-90ER40560

OSTI ID:: 1327326

Alternate ID(s):: OSTI ID: 22587679

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2016; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited By (5)

Chiral Gravitons in Fractional Quantum Hall Liquids Liou, Shiuan-Fan; Haldane, F. D. M.; Yang, Kun Physical Review Letters, Vol. 123, Issue 14 https://doi.org/10.1103/physrevlett.123.146801	journal	September 2019
Bimetric Theory of Fractional Quantum Hall States Gromov, Andrey; Son, Dam Thanh Physical Review X, Vol. 7, Issue 4 https://doi.org/10.1103/physrevx.7.041032	journal	November 2017
Towards Classification of Fracton Phases: The Multipole Algebra Gromov, Andrey Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/physrevx.9.031035	journal	August 2019
Bimetric Theory of Fractional Quantum Hall States Gromov, Andrey; Son, Dam Thanh arXiv https://doi.org/10.48550/arxiv.1705.06739	text	January 2017
Chiral Gravitons in Fractional Quantum Hall Liquids Liou, Shiuan-Fan; Haldane, F. D. M.; Yang, Kun arXiv https://doi.org/10.48550/arxiv.1904.12231	text	January 2019

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