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Spectral response functions are central quantities in the analysis of quantummany-body states, since they describe the response of many-body systems toexternal perturbations and hence directly correspond to observables inexperiments. In this paper, we evaluate a momentum-averaged dynamical densitystructure factor for the fermionic $\nu=1/3$ fractional quantum Hall state on atorus, using the continued fraction method to compute the dynamical correlationfunction. We establish the scaling behavior of the screened Coulomb structurefactor with respect to interaction range, and expose an inherentself-similarity of structure factors in the frequency domain. These resultshighlight the statistical properties of spectral response functions forfractional quantum Hall states and show how they can be efficientlyapproximated in numerical models.

Self-similarity of spectral response functions for fractional quantum Hall states