%0 Journal Article
%A Sanz, Mikel
%A Pérez García, David
%A Cirac, Juan I.
%A Wolf, Michael
%A González Guillén, Carlos Eduardo
%T A canonical form for Projected Entangled Pair States and applications
%D 2009
%@ 1367-2630
%U https://hdl.handle.net/20.500.14352/49543
%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.
%~