Spectral Sum Rules and Magneto-Roton as Emergent Graviton in Fractional Quantum Hall Effect
Sep 10, 2013
17 pages
Published in:
- JHEP 01 (2016) 021
- Published: Jan 5, 2016
e-Print:
- 1309.2638 [cond-mat.mes-hall]
Report number:
- EFI-13-22
Citations per year
Abstract: (Springer)
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 (ω) and , 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 , the q coefficient of the static structure factor S, and the high-frequency shear modulus of the ground state μ, which is precisely defined. We confirm an inequality, first suggested by Haldane, that S is bounded from below by . 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.Note:
- 17 pages, 2 figures
- Field Theories in Lower Dimensions
- Sum Rules
- Effective field theories
- density: spectral
- sum rule: spectral
- Hall effect: quantum
- graviton
- ground state
- gravitation: emergence
- Hall effect: fractional
References(22)
Figures(2)
- [1]
- [2]
- [3]
- [4]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [16]
- [17]
- [18]
- [19]
- [20]
- [21]
- [22]