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A canonical form for Projected Entangled Pair States and applications

D. Perez-Garcia, M. Sanz, C.E. Gonzalez-Guillen, M.M. Wolf, J.I. Cirac

New J. Phys. 12 025010 **, (2010)

DOI: 10.1088/1367-2630/12/2/025010 Pfeil
*arXiv.org*: 0908.1674 Pfeil

Abstract: 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.