%0 Journal Article
%A Pérez García, David
%A Sanz, M.
%A González-Guillén, C.M.
%A Wolf, M.M.
%A Cirac, J.I.
%T Characterizing symmetries in a projected entangled pair state
%D 2010
%@ 1367-2630
%U https://hdl.handle.net/20.500.14352/42478
%X 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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