TY - JOUR

T1 - Entanglement spectrum as a generalization of entanglement entropy

T2 - Identification of topological order in non-Abelian fractional quantum hall effect states

AU - Li, Hui

AU - Haldane, F. D.M.

PY - 2008/7/3

Y1 - 2008/7/3

N2 - 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 ν=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.

AB - 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 ν=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.

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U2 - 10.1103/PhysRevLett.101.010504

DO - 10.1103/PhysRevLett.101.010504

M3 - Article

C2 - 18764098

AN - SCOPUS:46949084674

VL - 101

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 1

M1 - 010504

ER -