A canonical form for Projected Entangled Pair States and applications
| dc.contributor.author | Sanz, Mikel | |
| dc.contributor.author | Pérez García, David | |
| dc.contributor.author | Cirac, Juan I. | |
| dc.contributor.author | Wolf, Michael | |
| dc.contributor.author | González Guillén, Carlos Eduardo | |
| dc.date.accessioned | 2023-06-20T09:26:34Z | |
| dc.date.available | 2023-06-20T09:26:34Z | |
| dc.date.issued | 2009 | |
| dc.description.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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea. FP7 | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/12163 | |
| dc.identifier.doi | 10.1088/1367-2630/12/2/025010 | |
| dc.identifier.issn | 1367-2630 | |
| dc.identifier.officialurl | http://arxiv.org/abs/0908.1674 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49543 | |
| dc.journal.title | New Journal of Physics | |
| dc.language.iso | eng | |
| dc.relation.projectID | QUEVADIS (233859) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.cdu | 530.145 | |
| dc.subject.keyword | Teoría cuántica | |
| dc.subject.keyword | Física matemática | |
| dc.subject.keyword | Quantum Physics | |
| dc.subject.keyword | Mathematical Physics | |
| dc.subject.ucm | Física matemática | |
| dc.subject.ucm | Teoría de los quanta | |
| dc.subject.unesco | 2210.23 Teoría Cuántica | |
| dc.title | A canonical form for Projected Entangled Pair States and applications | |
| dc.type | journal article | |
| dcterms.references | [1] A. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Commun. Math. Phys. 115, 477 (1988). [2] F. Verstraete and J. I. Cirac (2004), cond-mat/0407066; F. Verstraete, V. Murg, and J. I. Cirac, Advances in Physics 57, 143 (2008); N. Maeshima, Y. Hieida, Y. Akutsu, T. Nishino, K. Okunishi, Phys. Rev. E 64 (2001) 016705; Y. Nishio, N. Maeshima, A. Gendiar, T. Nishino, cond-mat/0401115 (2004). [3] M. B. Hastings, Phys. Rev. B 76, 035114 (2007); M. B. Hastings JSTAT, P08024 (2007); F. Verstraete, J.I. Cirac, Phys. Rev. B 73, 094423 (2006) [4] F. Verstraete, M.M. Wolf, D. P´erez-Garc´ıa, Phys. Rev. Lett 96, 220601 (2006). [5] O. Buerschaper, M. Aguado, G. Vidal, Phys. Rev. B 79, 085119 (2009) [6] E. Rico, H.J. Briegel, Ann. of Phys. 323:2115-2131 (2008). [7] D. Gross, J. Eisert, Phys. Rev. Lett. 98, 220503 (2007); D. Gross, J. Eisert, N. Schuch, D. Perez-Garcia, Phys. Rev. A 76, 052315 (2007) [8] E. Lieb, T. Schultz and D. Mattis, Ann. Phys. 16, 407 (1961). [9] M.B. Hastings, Phys.Rev. B69 (2004) 104431; B. Nachtergaele, R. Sims, Commun. Math. Phys. 276 (2007) 437–472. [10] M. Oshikawa, M. Yamanaka and I. Affleck, Phys. Rev. Lett. 78, 1984 (1997). [11] D. P´erez-Garc´ıa, M. M. Wolf, M. Sanz, F. Verstraete and J. I. Cirac, Phys. Rev. Lett. 100, 167202 (2008) [12] F. Anfuso, A. Rosch Phys. Rev. B 76, 085124 (2007). [13] M. Fannes, B. Nachtergaele and R. W. Werner, Comm. Math. Phys. 144, 443 (1992). [14] D. P´erez-Garc´ıa, F. Verstraete, M.M. Wolf, J.I. Cirac, Quantum Inf. Comput. 7, 401 (2007). [15] G. Vidal, Phys. Rev. Lett. 91, 147902 (2003). [16] N. Schuch, M. M. Wolf, F. Verstraete, J. I. Cirac, Phys. Rev. Lett. 98, 140506 (2007) [17] D. P´erez-Garc´ıa, F. Verstraete, J.I. Cirac and M.M. Wolf, Quant. Inf. Comp. 8, 0650-0663 (2008). [18] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press 1991. [19] S. Singh, R. N. C. Pfeifer, G. Vidal, arXiv:0907.2994. [20] M. Sanz, M.M. Wolf, D. P´erez-Garc´ıa and J. I. Cirac, Phys. Rev. A 79, 042308 (2009) [21] A. Yu. Kitaev, Annals Phys. 303 (2003) 2-30. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
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