2020/07/31 by Bartholomew Andrews, Madhav Mohan, Titus Neupert
Mathematics · Physics and Astronomy · #Abelian group #Algorithm #Combinatorics #Electron #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Topological order #Topology (electrical circuits) #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.103.075132
published as Phys. Rev. B 103, 075132 (2021) · 15 pages, 7 figures
openalex created_date 2020/07/23 · arxiv created 2021/02/18 · openalex publication_date 2021/02/18 · arxiv updated 2021/02/19 · openalex updated_date 2026/08/06
Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an indicator of Abelian statistics to investigate the single-component \ensuremathν=2/5 and 3/7 states for the Hofstadter model in the band mixing regime. We perform many-body simulations using the infinite cylinder density matrix renormalization group and present an efficient algorithm to construct the area law of entanglement, which accounts for both numerical and statistical errors. Using this algorithm, we show that the \ensuremathν=2/5 and 3/7 states exhibit Abelian topological order in the case of two-body nearest-neighbor interactions. Moreover, we discuss the sensitivity of the proposed method and fractional quantum Hall states with respect to interaction range and strength.