Bipartite fluctuations and entanglement spectrum in quantum Hall states

We exploit a general relation between bipartite fluctuations of particle number or spin and the real space bipartite entanglement entropy and the entanglement R\'enyi entropies for free fermion systems [Phys. Rev. B \textbf{85}, 035409 (2012)]. We apply this method to derive the real space entanglement entropy and entanglement spectrum [Phys. Rev. Lett. \textbf{101}, 010504 (2008)] of integer quantum Hall systems and Chern insulators, focusing on continuum models, edge models at quantum point contacts and the role of sine-Gordon terms, and finite-sized lattice models. Numerical efforts will be addressed for fractional quantum Hall systems.