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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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Official URL: http://arxiv.org/abs/0908.1674

## Abstract

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 |
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Uncontrolled Keywords: | Teoría cuántica, Física matemática, Quantum Physics, Mathematical Physics |

Subjects: | Sciences > Physics > Mathematical physics Sciences > Physics > Quantum theory |

ID Code: | 12163 |

Deposited On: | 03 Feb 2011 10:00 |

Last Modified: | 03 Dec 2014 08:41 |

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