Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications

Abstract

Neutral excitations in a fractional quantum Hall droplet define the incompressibility gap of the topological phase. In this work, we derived a set of analytical results for the energy gap of the graviton modes with two-body and three-body Hamiltonians in both the long-wavelength and thermodynamic limit. These allow us to construct model Hamiltonians for the graviton modes in different FQH phases, and to elucidate a hierarchical structure of conformal Hilbert spaces (nullspaces of model Hamiltonians) with respect to the graviton modes and their corresponding ground states. Using the analytical tools developed, we perform numerical analysis with a particular focus on the Laughlin $\nu =1/5$ and the Gaffnian $\nu =2/5$ phases. Our calculation shows that for gapped phases, low-lying neutral excitations can undergo a "phase transition" even when the ground state is invariant. We discuss the compressibility of the Gaffnian phase, the possibility of multiple graviton modes, and the transition from the graviton modes to the "hollow-core" modes, as well as their experimental consequences.

36 pages, 8 figures

References in corpus (14)

• Fractional Quantum Hall States and Jack Polynomials
• Observation of neutral modes in the fractional quantum Hall regime
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter $\alpha$
• Primary-Filling e/3 Quasiparticle Interferometer
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• Dirac Composite Fermion Theory of General Jain's Sequences
• Gaplessness of the Gaffnian

Cited by in corpus (9)

• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Supergravity model of the Haldane-Rezayi fractional quantum Hall state
• Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator
• Parametrization and thermodynamic scaling of pair correlation functions for the Fractional Quantum Hall Effect
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators