A numerical study of bounds in the correlations of fractional quantum Hall states

We numerically compute the guiding center static structure factor S(k) of various fractional quantum Hall (FQH) states to O ((kℓ)6) where k is the wavenumber and ℓ is the magnetic length. Employing density matrix renormalization group on an infinite cylinder of circumference Ly , we study the two-dimensional limit using Ly/ξ ≪ 1, where ξ is the correlation length. The main findings of our work are: 1) the ground states that deviate away from the ideal conformal block wavefunctions, do not saturate the Haldane bound, and 2) the coefficient of O ((kℓ)6) term appears to be bounded above by a value predicted by field theories proposed in the literature. The first finding implies that the graviton mode is not maximally chiral for experimentally relevant FQH states.