Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems

Abstract

We investigate the non-universal part of the orbital entanglement spectrum (OES) of the nu = 1/3 fractional quantum Hall effect (FQH) ground-state with Coulomb interactions. The non-universal part of the spectrum is the part that is missing in the Laughlin model state OES whose level counting is completely determined by its topological order. We find that the OES levels of the Coulomb interaction ground-state are organized in a hierarchical structure that mimic the excitation-energy structure of the model pseudopotential Hamiltonian which has a Laughlin ground state. These structures can be accurately modeled using Jain's "composite fermion" quasihole-quasiparticle excitation wavefunctions. To emphasize the connection between the entanglement spectrum and the energy spectrum, we also consider the thermodynamical OES of the model pseudopotential Hamiltonian at finite temperature. The observed good match between the thermodynamical OES and the Coulomb OES suggests a relation between the entanglement gap and the true energy gap.

16 pages, 19 figures

References in corpus (26)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Inversion Symmetric Topological Insulators
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum in one-dimensional systems
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Entanglement entropy in fermionic Laughlin states
• Bulk-Edge Correspondence in the Entanglement Spectra
• Entanglement spectra of quantum Heisenberg ladders
• Extracting Excitations From Model State Entanglement
• Topological phases and phase transitions on the square-octagon lattice
• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Entanglement spectrum of random-singlet quantum critical points
• Entanglement Spectrum and Entanglement Thermodynamics of Quantum Hall Bilayers at nu=1
• Entanglement spectrum of one-dimensional extended Bose-Hubbard models
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Entanglement spectra of complex paired superfluids
• Topological Entanglement in Abelian and non-Abelian Excitation Eigenstates
• Interaction-tuned compressible-to-incompressible phase transitions in the quantum Hall systems
• Haldane Statistics in the Finite Size Entanglement Spectra of Laughlin States
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Effective spin chains for fractional quantum Hall states
• Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization

Cited by in corpus (27)

• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Real-Space Entanglement Spectrum of Quantum Hall States
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Fractional Chern Insulators beyond Laughlin states
• Entanglement spectra of coupled S=1/2 spin chains in a ladder geometry
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Entanglement entropy of (3+1)D topological orders with excitations
• Tree tensor networks and entanglement spectra
• Matrix Product State description of the Halperin States
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Focus on topological quantum computation
• Emergence of Topological and Strongly Correlated Ground States in trapped Rashba Spin-Orbit Coupled Bose Gases
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Entanglement Entropy & Anomaly Inflow
• Entanglement Spectra and Entanglement Thermodynamics of Hofstadter Bilayers
• Energy projection and modified Laughlin states
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons
• Fractional Quantum Hall Matrix Product States For Interacting Conformal Field Theories
• Entanglement spectrum of fermionic bilayer honeycomb lattice: Hofstadter butterfly
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states