Pérez García, DavidSanz, M.González-Guillén, C.M.Wolf, M.M.Cirac, J.I.2023-06-202023-06-2020101367-263010.1088/1367-2630/12/2/025010https://hdl.handle.net/20.500.14352/42478We 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.engjournal articlehttp://iopscience.iop.org/1367-2630/12/2/025010http://iopscience.iop.org/open access53Física matemática