Analytic Wavefunctions for Neutral Bulk Excitations in Fractional Quantum Hall Fluids

Abstract

We show the model wavefunctions for the neutral collective modes in fractional quantum Hall (FQH) states have simple analytic forms obtained from judicially reducing the powers of selected pairs in the ground state Jastrow factor. This scheme of "pair excitations" works for the magneto-roton modes of single-component Abelian and non-Abeliean FQH states, as well as the neutral fermion mode for the Moore-Read (MR) state. The analytic wavefunctions allow us to compute the "quadrupole gap" of the magneto-roton mode in the thermodynamic limit, which was previously inaccessible to the numerics. The quadrupole gap is related to the fusion of the charges in the two-dimensional plasma picture, extending the plasma analogy to neutral excitations. A lattice diagrammatic method of representing these many-body wavefunctions and FQH elementary excitations is also presented.

an expanded version of arXiv:1303.6299, published in PRB

References in corpus (14)

• Fractional Quantum Hall States and Jack Polynomials
• Fractional Chern Insulators and the W-Infinity Algebra
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at $\nu =1/3$
• Unpaired composite fermion, topological exciton, and zero mode
• Quasiparticles and excitons for the Pfaffian quantum Hall state

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• Collective excitations at filling factor 5/2: The view from superspace
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples
• The Neutral Excitations in the Gaffnian State
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Hyperspherical approach to the three-bosons problem in 2D with a magnetic field
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• 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
• Spin of fractional quantum Hall neutral modes and "missing states" on a sphere