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.

arXiv comment10 pages, 7 figures, comments very welcome

References in corpus (43)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Geometrical Description of the Fractional Quantum Hall Effect
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Fractional Quantum Hall Effect of Composite Fermions
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Can Gravitons Be Detected?
• Landau Level Mixing and the Fractional Quantum Hall Effect
• A nu=2/5 Paired Wavefunction
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Properties of Non-Abelian Fractional Quantum Hall States at Filling $\nu =\frac{k}{r}$
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Paired composite fermion wavefunctions
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Chiral Gravitons in Fractional Quantum Hall Liquids
• Landau Level Mixing in the Perturbative Limit
• Generalized Quantum Hall Projection Hamiltonians
• Spectral Sum Rules and Magneto-Roton as Emergent Graviton in Fractional Quantum Hall Effect
• Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2
• Landau Level Mixing and Levitation of Extended States in Two Dimensions
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Acoustic Wave Absorption as a Probe of Dynamical Geometrical Response of Fractional Quantum Hall Liquids
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State
• Microscopic theory for nematic fractional quantum Hall effect
• Collective excitations at filling factor 5/2: The view from superspace
• Dirac Composite Fermion Theory of General Jain's Sequences
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• Gapped Excitations of unconventional FQHE states in the Second Landau Level
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Noncommutative Chern-Simons theory and exotic geometry emerging from the lowest Landau level
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Fractional quantum Hall effect from frustration-free Hamiltonians

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• 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