Topological Entanglement in Abelian and non-Abelian Excitation Eigenstates

Abstract

Entanglement in topological phases of matter has so far been investigated through the perspective of their ground-state wave functions. In contrast, we demonstrate that the \emph{excitations} of fractional quantum Hall (FQH) systems also contain information to identify the system's topological order. Entanglement spectrum of the FQH quasihole (QH) excitations is shown to differentiate between the conformal field theory (CFT) sectors, based on the relative position of the QH with respect to the entanglement cut. For Read-Rezayi model states, as well as Coulomb interaction eigenstates, the counting of the QH entanglement levels in the thermodynamic limit matches exactly the CFT counting, and sector changes occur as non-Abelian quasiholes successively cross the entanglement cut.

arXiv comment4 pages, 7 figures

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• Trace Index and Spectral Flow in the Entanglement Spectrum
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• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Evaluation of ranks of real space and particle entanglement spectra for large systems
• Flux insertion, entanglement, and quantized responses
• Adiabatic continuity between Hofstadter and Chern insulator states
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Bound states and entanglement in the excited states of quantum spin chains
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Fluctuations and Entanglement spectrum in quantum Hall states
• Entanglement Spectroscopy using Quantum Monte Carlo
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• 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
• Entanglement spectrum of the Heisenberg XXZ chain near the ferromagnetic point
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Topological Characterization of Non-Abelian Moore-Read State using Density-Matrix Renormailzation Group
• Landau Levels in Strained Optical Lattices
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Entanglement Measures for Quasi-Two-Dimensional Fractional Quantum Hall States
• Bootstrapping the Quantum Hall problem
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Temporal Entanglement Transitions in the Periodically Driven Ising Chain