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

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.