Equipartition of Entanglement in Quantum Hall States

Abstract

We study the full counting statistics (FCS) and symmetry-resolved entanglement entropies of integer and fractional quantum Hall states. For the filled lowest Landau level of spin-polarized electrons on an infinite cylinder, we compute exactly the charged moments associated with a cut orthogonal to the cylinder's axis. This yields the behavior of FCS and entropies in the limit of large perimeters: in a suitable range of fluctuations, FCS is Gaussian and entanglement spreads evenly among different charge sectors. Subleading charge-dependent corrections to equipartition are also derived. We then extend the analysis to Laughlin wavefunctions, where entanglement spectroscopy is carried out assuming the Li-Haldane conjecture. The results confirm equipartition up to small charge-dependent terms, and are then matched with numerical computations based on exact matrix product states.

15 pages, 16 figures. v2: Minor cosmetic alterations, published in Phys. Rev. B

References in corpus (18)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• The entanglement entropy of one-dimensional gases
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Entanglement and symmetry resolution in two dimensional free quantum field theories
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Entanglement equipartition in critical random spin chains
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• Symmetry decomposition of relative entropies in conformal field theory
• Branch Point Twist Field Form Factors in the sine-Gordon Model II: Composite Twist Fields and Symmetry Resolved Entanglement
• Charged Renyi entropies and holographic superconductors
• Fluctuations and Entanglement spectrum in quantum Hall states
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Entanglement entropy of integer Quantum Hall states in polygonal domains
• Matrix product state representation of non-Abelian quasiholes
• Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals
• Ergodic Edge Modes in the 4D Quantum Hall Effect
• Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions

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