A canonical form for Projected Entangled Pair States and applications

Details A canonical form for Projected Entangled Pair States and applications A canonical form for Projected Entangled Pair States and applications

2009-08-12

arxiv.org/abs/0908.1674v1

New J. Phys. 12 (2010) 025010

Physics

Quantum Physics

10 pages, 16 figures

Scientific paper

10.1088/1367-2630/12/2/025010

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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