Entanglement action for the real-space entanglement spectra of chiral Abelian quantum Hall wave functions

Abstract

We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of chiral Abelian quantum Hall states is given by the spectrum of a local boundary perturbation of a $(1+1)$-dimensional conformal field theory, which describes an effective edge dynamics along the real-space cut. The cut-and-glue approach suggests that the low-lying RSES is equivalent to the low-lying modes of some effective edge action. The general structure of this action is deduced by mapping to a boundary critical problem, generalizing the work of Dubail, Read, and Rezayi [Phys. Rev. B 85, 115321 (2012)]. Using trial wave functions, we numerically test our model of the RSES for the $\ensuremath{\nu}=2/3$ bosonic composite fermion state.