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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 wave functions, 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.
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Submitted on : Tuesday, January 18, 2022 - 10:17:54 AM
Last modification on : Tuesday, May 17, 2022 - 4:55:58 AM

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Blagoje Oblak, Nicolas Regnault, Benoit Estienne. Equipartition of entanglement in quantum Hall states. Phys.Rev.B, 2022, 105 (11), pp.115131. ⟨10.1103/PhysRevB.105.115131⟩. ⟨hal-03531207⟩

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