Equipartition of Entanglement in Quantum Hall States

TL;DR

This paper analyzes the entanglement and full counting statistics in quantum Hall states, showing equipartition of entanglement among charge sectors and deriving charge-dependent corrections through exact and numerical methods.

Contribution

It provides an exact computation of charged moments and entanglement properties in quantum Hall states, extending to Laughlin wavefunctions and confirming equipartition with small corrections.

Findings

FCS is Gaussian in large perimeter limit

Entanglement spreads evenly among charge sectors

Charge-dependent corrections to equipartition are small

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.