Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States

We study the “entanglement spectrum” (a presentation of the Schmidt decomposition analogous to a set of “energy levels”) of a many-body state, and compare the Moore-Read model wave function for the $\nu =5/2$ fractional quantum Hall state with a generic $5/2$ state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common “gapless” structure, related to conformal field theory. In the model state, these are the only levels, while in the “generic” case, they are separated from the rest of the spectrum by a clear “entanglement gap”, which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a “fingerprint” to identify topological order.