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Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems.
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Verstraete, F. , Wolf, M. M., Perez-Garcia, D. and Cirac, J. I.: Criticality, the area law, and the computational power of PEPS. Phys. Rev. Lett. 96, 220601 (2006)
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Cirac, J. I., Poilblanc, D., Schuch, N., and Verstraete, F.: Entanglement spectrum and boundary theories with projected entangled-pair states. Physical Review B, 83(24):245134, 2011
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Schuch, N., Perez-Garcia, D., Cirac, J.I.: Classifying quantum phases using matrix product states and projected entangled pair states. Physical Review B, 84(16):165139, 2011
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Li, H. and Haldane, F. D. M.: Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states. Physical Review Letters, 101(1):010504, 2008
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Perez-Garcia, D., Sanz, M., Gonzalez-Guillen, C.E., Wolf, M.M. and Cirac, J.I.: Characterizing symmetries in a projected entangled pair state. New Journal of Physics, 12(2), 025010 (2010)
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Anshu, A. , Arad, I., Vidick, T.: A simple proof of the detectability lemma and spectral gap amplification. Phys. Rev. B 93, 205142 (2016)
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Cirac, J. I., Perez-Garcia, D., Schuch, N., Verstraete, F.: Matrix product denity operators: Renormalization fixed points and boundary theories. Annals of Physics, 378:100Ð149, 2017
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Cirac, J. I., Perez-Garcia, D., Schuch, N., Verstraete, F.: Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants. J. Stat. Mech. (2017) 083105
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Molnar, A., Garre-Rubio, J., Perez-Garcia, D., Schuch, N. and Cirac, J. I.: Normal projected entangled pair states generating the same state. New J. Phys. 20, 113017 (2018)
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Molnar, A., Ge, Y., Schuch, N. and Cirac, J.I.: A generalization of the injectivity condition for projected entangled pair states. J. Math. Phys. 59, 021902 (2018)
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Sahinoglu, M. B., Shukla, S. K., Bi, F. and Chen, X.: Matrix Product Representation of Locality Preserving Unitaries. Phys. Rev. B 98, 245122 (2018)
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