A canonical form for Projected Entangled Pair States and applications

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Perez-Garcia, D.
Sanz, M.
Gonzalez-Guillen, C. E.
Wolf, M. M.
Cirac, J. I.
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Abstract
Description
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.
Comment: 10 pages, 16 figures
Keywords
Quantum Physics, Condensed Matter - Strongly Correlated Electrons
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