Publication: A canonical form for Projected Entangled Pair States and applications
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2009
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We show that two different tensors defining the same translational invariant injective Projected Entangled Pair State (PEPS) in a square lattice must be the same up to a trivial gauge freedom. This allows us to characterize the existence of any local or spatial symmetry in the state. As an application of these results we prove that a SU(2) invariant PEPS with half-integer spin cannot be injective, which can be seen as a Lieb-Shultz-Mattis theorem in this context. We also give the natural generalization for U(1) symmetry in the spirit of Oshikawa-Yamanaka-Affleck, and show that a PEPS with Wilson loops cannot be injective.
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[1] A. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. 115, 477 (1988).
[2] F. Verstraete and J. I. Cirac (2004), cond-mat/0407066; F. Verstraete, V. Murg, and J. I. Cirac, Advances in Physics 57, 143 (2008); N. Maeshima, Y. Hieida, Y. Akutsu, T. Nishino, K. Okunishi, Phys. Rev. E 64 (2001) 016705; Y. Nishio, N. Maeshima, A. Gendiar, T. Nishino, cond-mat/0401115 (2004).
[3] M. B. Hastings, Phys. Rev. B 76, 035114 (2007); M. B. Hastings JSTAT, P08024 (2007); F. Verstraete, J.I. Cirac, Phys. Rev. B 73, 094423 (2006)
[4] F. Verstraete, M.M. Wolf, D. P´erez-Garc´ıa, Phys. Rev. Lett 96, 220601 (2006).
[5] O. Buerschaper, M. Aguado, G. Vidal, Phys. Rev. B 79, 085119 (2009)
[6] E. Rico, H.J. Briegel, Ann. of Phys. 323:2115-2131 (2008).
[7] D. Gross, J. Eisert, Phys. Rev. Lett. 98, 220503 (2007); D. Gross, J. Eisert, N. Schuch, D. Perez-Garcia, Phys. Rev. A 76, 052315 (2007)
[8] E. Lieb, T. Schultz and D. Mattis, Ann. Phys. 16, 407 (1961).
[9] M.B. Hastings, Phys.Rev. B69 (2004) 104431; B. Nachtergaele, R. Sims, Commun. Math. Phys. 276 (2007) 437–472.
[10] M. Oshikawa, M. Yamanaka and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997).
[11] D. P´erez-Garc´ıa, M. M. Wolf, M. Sanz, F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 100, 167202 (2008)
[12] F. Anfuso, A. Rosch Phys. Rev. B 76, 085124 (2007). [13] M. Fannes, B. Nachtergaele and R. W. Werner, Comm. Math. Phys. 144, 443 (1992).
[14] D. P´erez-Garc´ıa, F. Verstraete, M.M. Wolf, J.I. Cirac, Quantum Inf. Comput. 7, 401 (2007).
[15] G. Vidal, Phys. Rev. Lett. 91, 147902 (2003).
[16] N. Schuch, M. M. Wolf, F. Verstraete, J. I. Cirac, Phys. Rev. Lett. 98, 140506 (2007)
[17] D. P´erez-Garc´ıa, F. Verstraete, J.I. Cirac and M.M. Wolf, Quant. Inf. Comp. 8, 0650-0663 (2008).
[18] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press 1991. [19] S. Singh, R. N. C. Pfeifer, G. Vidal, arXiv:0907.2994.
[20] M. Sanz, M.M. Wolf, D. P´erez-Garc´ıa and J. I. Cirac, Phys. Rev. A 79, 042308 (2009)
[21] A. Yu. Kitaev, Annals Phys. 303 (2003) 2-30.