Spin of fractional quantum Hall neutral modes and "missing states" on a sphere

Abstract

A low-energy neutral quasiparticle in a fractional quantum Hall system appears in the latter's energy spectrum on a sphere as a series of many-body excited states labeled by the angular momentum $L$ and whose energy is a smooth function of $L$ in the limit of large sphere radius. We argue that the signature of a nonvanishing spin (intrinsic angular momentum) $s$ of the quasiparticle is the absence, in this series, of states with total angular momentum less than $s$.We reinterpret the missing of certain states, observed in an exact-diagonalization calculation of the spectrum of the $\nu =7/3$ FQH state in a wide quantum well as well as in many proposed wave functions for the excited states as a consequence of the spin-2 nature of the zero-momentum magnetoroton.

10 pages. Updated version with minor revisions. Comments are welcome!

References in corpus (9)

• 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
• Shape of the magnetoroton at $\nu =1/3$ and $\nu =7/3$ in real samples
• Supergravity model of the Haldane-Rezayi fractional quantum Hall state
• Signatures of Supersymmetry in the $\nu =5/2$ Fractional Quantum Hall Effect
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Magnetorotons in Moiré Fractional Chern Insulators
• Analytic Wavefunctions for Collective Modes in Fractional Quantum Hall Fluids