Inner Nonlinear Waves and Inelastic Light Scattering of Fractional Quantum Hall States as Evidence of the Gravitational Anomaly

Abstract

We develop the quantum hydrodynamics of inner waves in the bulk of fractional quantum Hall states. We show that the inelastic light scattering by inner waves is a sole effect of the gravitational anomaly. We obtain the formula for the oscillator-strength or mean energy of optical absorption expressed solely in terms of an independently measurable static structure factor. The formula does not explicitly depend on a model interaction potential.

6 pages, v.2 minor changes in introduction and display of equations

References in corpus (5)

• Observed Quantization of Anyonic Heat Flow
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Bimetric Theory of Fractional Quantum Hall States
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples

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• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• Gravitational vortex mass in a superfluid
• W-infinity Symmetry in the Quantum Hall Effect Beyond the Edge
• Geometric description of the Kitaev honeycomb lattice model
• Anomalous chiral transport with vorticity and torsion: Cancellation of two mixed gravitational anomaly currents in rotating chiral $p+ip$ Weyl condensates
• Bulk-Boundary Correspondence in the Quantum Hall Effect
• Geometry induced quantum Hall effect and Hall viscosity
• Geometric and computational aspects of chiral topological quantum matter