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A canonical form for Projected Entangled Pair States and applications

Sanz, Mikel and Pérez García, David and Cirac, Juan I. and Wolf, Michael and González Guillén, Carlos Eduardo (2009) A canonical form for Projected Entangled Pair States and applications. New Journal of Physics . ISSN 1367-2630


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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.

Item Type:Article
Uncontrolled Keywords:Teoría cuántica, Física matemática, Quantum Physics, Mathematical Physics
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:12163

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