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Characterizing symmetries in a projected entangled pair state



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Pérez García, David and Sanz, M. and González-Guillén, C.M. and Wolf, M.M. and Cirac, J.I. (2010) Characterizing symmetries in a projected entangled pair state. New Journal of Physics, 12 . pp. 1-19. ISSN 1367-2630


Official URL: http://iopscience.iop.org/1367-2630/12/2/025010



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.

Item Type:Article
Subjects:Sciences > Physics > Mathematical physics
ID Code:17666
Deposited On:15 Jan 2013 09:28
Last Modified:03 Dec 2014 09:15

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