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

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.

arXiv comment8+9 pages, 2+4 figures

References in corpus (27)

• Response functions and Spectrum of Collective Excitations of Fractional Quantum Hall Effect Systems
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• Electrical generation and detection of spin waves in a quantum Hall ferromagnet
• Chiral Gravitons in Fractional Quantum Hall Liquids
• Lanczos algorithm with Matrix Product States for dynamical correlation functions
• Spectral Sum Rules and Magneto-Roton as Emergent Graviton in Fractional Quantum Hall Effect
• Response Function of the Fractional Quantized Hall State on a Sphere II: Exact Diagonalization
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Lattice Monte Carlo for Quantum Hall States on a Torus
• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems
• Dynamical structure factors of dynamical quantum simulators
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• Composite Fermions on a Torus
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Trial wave functions for a Composite Fermi liquid on a torus
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Effective Abelian theory from a non-Abelian topological order in $\nu =2/5$ fractional quantum Hall effect
• First-principles characterization of the magnetic properties of Cu${}_2$(OH)${}_3$Br
• Hierarchical Wave Functions and Fractional Statistics in Fractional Quantum Hall Effect on the Torus
• Composite anyons on a torus
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Dynamical screening in SrVO${}_3$: Inelastic x-ray scattering experiments and ab initio calculations
• Dynamical Structure Factor of Fulde-Ferrell-Larkin-Ovchinnikov Superconductors

Cited by in corpus (3)

• Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method
• Localization renormalization and quantum Hall systems
• Physically interpretable approximations of many-body spectral functions