Entanglement Action for the Real-Space Entanglement Spectra of Composite Fermion Wave Functions

TL;DR

This paper demonstrates that the real-space entanglement spectrum of composite fermion quantum Hall states can be modeled by a local boundary perturbation of a conformal field theory, linking entanglement properties to edge dynamics.

Contribution

It introduces a theoretical framework connecting the RSES of composite fermion states to boundary conformal field theories and validates it with numerical tests.

Findings

RSES corresponds to a boundary perturbation of a 1+1D CFT.

The low-lying RSES matches the spectrum of an effective edge action.

Numerical tests confirm the model for the ν=2/3 bosonic state.

Abstract

We argue and numerically substantiate that the real-space entanglement spectrum (RSES) of composite fermion quantum Hall states is given by the spectrum of a local boundary perturbation of a $(1+1)$d conformal field theory (CFT), 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 work of Dubail, Read, and Rezayi [PRB 85, 11531 (2012)]. Using trial wave functions we numerically test our model of the RSES for the $\nu = 2/3$ bosonic composite fermion state.