Journal
NEW JOURNAL OF PHYSICS
Volume 12, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/12/2/025010
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Funding
- DFG [FOR 635]
- I-MATH [MTM2008-01366, CCG08-UCM/ESP-4394]
- QUANTOP
- Danish Natural Science Research Council(FNU)
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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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