Self-similarity of spectral response functions for fractional quantum Hall states with long-range interactions

Abstract

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 ν = 1/3 fractional quantum Hall state on a torus, using the continued fraction method to compute the dynamical correlation function. We highlight the discrepancy between the structure factors corresponding to the short-range V1 and long-range Coulomb interactions, despite both models yielding ground states in the same universality class. Motivated by this, we establish a scaling relation for the screened Coulomb structure factor with respect to interaction range, and expose an inherent self-similarity of structure factors for long-range interactions in the frequency domain. Finally, we demonstrate that Haldane pseudopotentials may be used to approximate the structure factor for long-range interactions on the torus, provided that the interaction is sufficiently screened. These results highlight the self-similar properties of spectral response functions for fractional quantum Hall states with long-range interactions and show how they can be efficiently approximated in numerical models.