  Spectral response functions are central quantities in the analysis of quantum
many-body states, since they describe the response of many-body systems to
external perturbations and hence directly correspond to observables in
experiments. In this paper, we evaluate a momentum-averaged dynamical density
structure factor for the fermionic $\nu=1/3$ fractional quantum Hall state on a
torus, using the continued fraction method to compute the dynamical correlation
function. We establish the scaling behavior of the screened Coulomb structure
factor with respect to interaction range, and expose an inherent
self-similarity of structure factors in the frequency domain. These results
highlight the statistical properties of spectral response functions for
fractional quantum Hall states and show how they can be efficiently
approximated in numerical models.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics