Equipartition of entanglement in quantum Hall states

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.

Automated summary

In this study, we investigate the full counting statistics (FCS) and symmetry-resolved entanglement entropies of integer and fractional quantum Hall states. The behavior of FCS and entanglement entropies in the limit of large perimeters is obtained by computing the charged moments associated with a cut orthogonal to the cylinder's axis. The results show that FCS follows a Gaussian distribution and entanglement spreads evenly among different charge sectors. Subleading charge-dependent corrections and entanglement spectroscopy are also analyzed and matched with numerical computations.