Edge-mode combinations in the entanglement spectra of non-Abelian fractional quantum Hall states on the torus

2011/09/30 by Zhao Liu, Emil J. Bergholtz, Heng Fan +2 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Abelian group #Boson #Composite fermion #Conformal field theory #Conformal map #Fermion #Fractional quantum Hall effect #Geometry #Magnetic field #Mathematics #Physics #Pure mathematics #Quantum #Quantum Hall effect #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #Torus #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.85.045119

published as Phys. Rev. B 85, 045119 (2012) · 13 pages, 8 figures, published version on PRB

arxiv created 2012/01/19 · openalex publication_date 2012/01/19 · arxiv updated 2012/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a detailed analysis of bipartite entanglement in the non-Abelian Moore-Read fractional quantum Hall state of bosons and fermions on the torus. In particular, we show that the entanglement spectra can be decomposed into intricate combinations of different sectors of the conformal field theory describing the edge physics, and that the edge level counting and tower structure can be microscopically understood by considering the vicinity of the thin-torus limit. We also find that the boundary entropy density of the Moore-Read state is markedly higher than in the Laughlin states investigated so far. Despite the torus geometry being somewhat more involved than in the sphere geometry, our analysis and insights may prove useful when adopting entanglement probes to other systems that are more easily studied with periodic boundary conditions, such as fractional Chern insulators and lattice problems in general.

Citations

• Colloquium: Area laws for the entanglement entropy
• Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros
• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Many-body physics with ultracold gases
• Entanglement spectrum of one-dimensional extended Bose-Hubbard models
• Incompressible Quantum Liquids and New Conservation Laws
• Density-matrix algorithms for quantum renormalization groups
• Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Criticality, the area law, and the computational power of PEPS
• Quantum Hall Fractions in Rotating Bose-Einstein Condensates
• Entanglement spectrum of a topological phase in one dimension
• Ground-State Phase Diagram of 2D Electrons in a High Landau Level: A Density-Matrix Renormalization Group Study
• Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory
• Entanglement spectrum in one-dimensional systems
• Class of Quantum Many-Body States That Can Be Efficiently Simulated
• Simulation of interacting fermions with entanglement renormalization
• Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law
• Entanglement Entropy and Entanglement Spectrum of the Kitaev Model
• Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries
• Non-Abelian anyons and topological quantum computation
• The density-matrix renormalization group
• Nonabelions in the fractional quantum hall effect
• A Modular Functor Which is Universal¶for Quantum Computation
• Entanglement in many-body systems

Cited by

• Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models
• Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe