Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect

Abstract

We construct model wavefunctions for the collective modes of fractional quantum Hall systems. The wavefunctions are expressed in terms of symmetric polynomials characterized by a root partition and a "squeezed" basis, and show excellent agreement with exact diagonalization results for finite systems. In the long wavelength limit, the model wavefunctions reduce to those predicted by the single-mode approximation, and remain accurate at energies above the continuum of roton pairs.

4 pages, 3 figures, minor changes for the final prl version

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Cited by in corpus (79)

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• Higher-Spin Theory of the Magnetorotons
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• Exactly Solvable Fermion Chain Describing a $\nu =1/3$ Fractional Quantum Hall State
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• Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Acoustic Wave Absorption as a Probe of Dynamical Geometrical Response of Fractional Quantum Hall Liquids
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• 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
• Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Enhanced fractional quantum Hall gaps in a two-dimensional electron gas coupled to a hovering split-ring resonator
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study
• Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers
• Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in the Laughlin Quantum Hall Fluids
• Microscopic theory for nematic fractional quantum Hall effect
• Microscopic Model for Fractional Quantum Hall Nematics
• Construction of the edge states in fractional quantum Hall systems by Jack polynomial
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Collective excitations at filling factor 5/2: The view from superspace
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• Analytic Wavefunctions for Neutral Bulk Excitations in Fractional Quantum Hall Fluids
• Emergent Commensurability from Hilbert Space Truncation in Fractional Quantum Hall Fluids
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• Low-complexity eigenstates of a $\nu =1/3$ fractional quantum Hall system
• Inner Nonlinear Waves and Inelastic Light Scattering of Fractional Quantum Hall States as Evidence of the Gravitational Anomaly
• Noncommutative Chern-Simons theory and exotic geometry emerging from the lowest Landau level
• Geometric responses of the Pfaffian state
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• The Neutral Excitations in the Gaffnian State
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• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Fractionalisation and dynamics of anyons at $\nu =n+1/3$ in fractional quantum Hall effect and their experimental signatures
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• The spectral gap of a fractional quantum Hall system on a thin torus
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Phase diagram of $\nu =\frac{1}{2}+\frac{1}{2}$ bilayer bosons with inter-layer couplings
• Spectra of Magnetoroton and Chiral Graviton Modes of Fractional Chern Insulator
• Moiré Assisted Fractional Quantum Hall State Spectroscopy
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Parametrization and thermodynamic scaling of pair correlation functions for the Fractional Quantum Hall Effect
• Neutral excitation and bulk gap of the Fractional Quantum Hall liquids in disk geometry
• Deformed Fredkin model for the $\nu =5/2$ Moore-Read state on thin cylinders
• The composite fermion theory revisited: a microscopic derivation without Landau level projection
• Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
• Fractional Quantum Hall Effect Based on Weyl Orbits
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Collective excitations of quantum Hall states under tilted magnetic field
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• Gauge-Invariant Variables Reveal the Quantum Geometry of Fractional Quantum Hall States
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
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• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Exact Mappings in Condensed Matter Physics
• Chiral Graviton Modes in Fermionic Fractional Chern Insulators
• Spin of fractional quantum Hall neutral modes and "missing states" on a sphere
• Developments in the applications of density functional theory to fractional quantum Hall systems