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

Journal Article · Tue Jan 05 00:00:00 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. ^[1]; Son, Dam T. ^[1]

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1. 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.

• Research Organization: Univ. of Chicago, IL (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-90ER40560
• OSTI ID: 1327326
• Journal Information: Journal of High Energy Physics (Online), Vol. 2016, Issue 1; ISSN 1029-8479
• Publisher: Springer Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
field theories in lower dimensions
sum rules
effective field theories