Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect

Abstract

Neutral excitations in fractional quantum Hall (FQH) fluids define the incompressibility of topological phases, a species of which can show graviton-like behaviors and are thus called the graviton modes (GMs). Here, we develop the microscopic theory for multiple GMs in FQH fluids and show explicitly that they are associated with the geometric fluctuation of well-defined conformal Hilbert spaces (CHSs), which are hierarchical subspaces within a single Landau level, each with emergent conformal symmetry and continuously parameterized by a unimodular metric. This leads to several statements about the number and the merging/splitting of GMs, which are verified numerically with both model and realistic interactions. We also discuss how the microscopic theory can serve as the basis for the additional Haldane modes in the effective field theory description and their experimental relevance to realistic electron-electron interactions.

10 pages, 7 figures, comments very welcome

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Cited by in corpus (12)

• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator
• Self-similarity of spectral response functions for fractional quantum Hall states
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Dispersion of neutral collective modes in partonic fractional quantum Hall states and its applications to paired states of composite fermions
• Robust translational invariance in topological bands against lattice potentials and disorders
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators