A canonical form for Projected Entangled Pair States and applications
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 applicati...
| Autores: | , , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49543 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/49543 |
| Access Level: | acceso abierto |
| Palavra-chave: | 51-73 530.145 Teoría cuántica Física matemática Quantum Physics Mathematical Physics Teoría de los quanta 2210.23 Teoría Cuántica |
| Resumo: | 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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