A numerical study of bounds in the correlations of fractional quantum Hall states
We numerically compute the guiding center static structure factor \bar S(k) S βΎ ( k ) of various fractional quantum Hall (FQH) states to \mathcal{O}(k\ell)^6 πͺ ( k β ) 6 where k k is the wavenumber and \ell β is the magnetic length. Employing density matrix renormalization group on an infinite cylinder of circumference L_y L y , we study the two-dimensional limit using L_y/\xi \gg 1 L y / ΞΎ β« 1 , where \xi ΞΎ 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\ell)^6 O ( k β ) 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.