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Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
Open accessAbstract
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.
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Citations
Cites
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
Laughlin, R. B. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.1395 · Cited by 5,749
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
Haldane, F. D. M. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.605 · Cited by 2,210
Self-citation
Cited by
Colloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Entanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688
Higher-order topological insulators
Schindler, F., Cook, A. M., Vergniory, M. G., Wang, Z., Parkin, S. S. P., Bernevig, B. A., & Neupert, T. (2018) · Science Advances · doi:10.1126/sciadv.aat0346 · Cited by 1,618
Towards a derivation of holographic entanglement entropy
Casini, H., Huerta, M., & Myers, R. C. (2011) · Journal of High Energy Physics · doi:10.1007/jhep05(2011)036 · Cited by 1,347
Metadata
- Authors
- Li, H., & Haldane, F. D. M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-07-03
- Volume
- 101
- Issue
- 1
- Pages
- 010504-010504
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2082257352
- Cited by
- 1,652
- References
- 3
- FWCI
- 20.69
- Type
- journal article
- Language
- en
- Open access
- green
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- Li, H., & Haldane, F. D. M. (2008). Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States. Physical Review Letters. https://doi.org/10.1103/physrevlett.101.010504
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