English

A canonical form for Projected Entangled Pair States and applications

Quantum Physics 2014-04-11 v1 Strongly Correlated Electrons

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.

Keywords

Cite

@article{arxiv.0908.1674,
  title  = {A canonical form for Projected Entangled Pair States and applications},
  author = {D. Perez-Garcia and M. Sanz and C. E. Gonzalez-Guillen and M. M. Wolf and J. I. Cirac},
  journal= {arXiv preprint arXiv:0908.1674},
  year   = {2014}
}

Comments

10 pages, 16 figures