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.
Keywords
Cite
@article{arxiv.2112.13854,
title = {Equipartition of Entanglement in Quantum Hall States},
author = {Blagoje Oblak and Nicolas Regnault and Benoit Estienne},
journal= {arXiv preprint arXiv:2112.13854},
year = {2022}
}
Comments
15 pages, 16 figures. v2: Minor cosmetic alterations, published in Phys. Rev. B