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

We numerically compute the guiding center static structure factor S(k) S‾(k) of various fractional quantum Hall (FQH) states to O(k)^6 𝒪(kℓ)6 where k k is the wavenumber and ℓ is the magnetic length. Employing density matrix renormalization group on an infinite cylinder of circumference L_y Ly , we study the two-dimensional limit using L_y/ξ 1 Ly/ξ≫1 , where ξ 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(k)^6 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.