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

TL;DR

This paper investigates the spectral response functions of fractional quantum Hall states, revealing self-similarity and scaling behaviors that enhance understanding and modeling of these complex quantum systems.

Contribution

It demonstrates the self-similarity of spectral response functions and their scaling behavior in fractional quantum Hall states, providing insights for numerical approximations.

Findings

Self-similarity of structure factors in frequency domain

Scaling behavior of Coulomb structure factor with interaction range

Efficient numerical approximation of spectral response functions

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 $\nu=1/3$ 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.