Equipartition of Entanglement in Quantum Hall States

Quantum Hall effects provide an ideal playground to test the equipartition of entanglement for two-dimensional non-interacting and interacting gapped systems. We will discuss 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 will show that FCS is Gaussian and entanglement spreads evenly among different charge sectors. Moreover, finite size corrections can be derived. Moving to the interacting Laughlin state, the entanglement spectroscopy can be 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.