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

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