Sanz, MikelPérez García, DavidCirac, Juan I.Wolf, MichaelGonzález Guillén, Carlos Eduardo2023-06-202023-06-2020091367-263010.1088/1367-2630/12/2/025010https://hdl.handle.net/20.500.14352/49543We 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://arxiv.org/abs/0908.1674open access51-73530.145Teoría cuánticaFísica matemáticaQuantum PhysicsMathematical PhysicsFísica matemáticaTeoría de los quanta2210.23 Teoría Cuántica