Characterizing symmetries in a projected entangled pair state
| dc.contributor.author | Pérez García, David | |
| dc.contributor.author | Sanz, M. | |
| dc.contributor.author | González-Guillén, C.M. | |
| dc.contributor.author | Wolf, M.M. | |
| dc.contributor.author | Cirac, J.I. | |
| dc.date.accessioned | 2023-06-20T00:22:37Z | |
| dc.date.available | 2023-06-20T00:22:37Z | |
| dc.date.issued | 2010 | |
| 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.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | QCCC Program of the EliteNetzWerk Bayern | |
| dc.description.sponsorship | DFG (FOR 635, MAP and NIM) | |
| dc.description.sponsorship | Danish Natural Science Research Council(FNU) | |
| dc.description.sponsorship | QUANTOP | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17666 | |
| dc.identifier.doi | 10.1088/1367-2630/12/2/025010 | |
| dc.identifier.issn | 1367-2630 | |
| dc.identifier.officialurl | http://iopscience.iop.org/1367-2630/12/2/025010 | |
| dc.identifier.relatedurl | http://iopscience.iop.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42478 | |
| dc.journal.title | New Journal of Physics | |
| dc.language.iso | eng | |
| dc.page.final | 19 | |
| dc.page.initial | 1 | |
| dc.publisher | IOP | |
| dc.relation.projectID | I-MATH | |
| dc.relation.projectID | (MTM2008-01366) | |
| dc.relation.projectID | (CCG08-UCM/ESP-4394) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 53 | |
| dc.subject.ucm | Física matemática | |
| dc.title | Characterizing symmetries in a projected entangled pair state | |
| dc.type | journal article | |
| dc.volume.number | 12 | |
| dcterms.references | [1] Affleck A, Kennedy T, Lieb E H and Tasaki H 1988 Commun. Math. Phys. 115 477 [2] Verstraete F and Cirac J I 2004 arXiv:cond-mat/0407066 Verstraete F, Murg V and Cirac J I 2008 Adv. Phys. 57 143 Maeshima N, Hieida Y, Akutsu Y, Nishino T and Okunishi K 2001 Phys. Rev. E 64 016705 Nishio Y, Maeshima N, Gendiar A and Nishino T 2004 arXiv:cond-mat/0401115 [3] Hastings M B 2007 Phys. Rev. B 76 035114 Hastings M B 2007 J. Stat. P08024 Verstraete F and Cirac J I 2006 Phys. Rev. B 73 094423 [4] Verstraete F, Wolf M M and Pérez-García D 2006 Phys. Rev. Lett. 96 220601 [5] Buerschaper O, Aguado M and Vidal G 2009 Phys. Rev. B 79 085119 [6] Rico E and Briegel H J 2008 Ann. Phys. 323 2115–31 [7] Gross D and Eisert J 2007 Phys. Rev. Lett. 98 220503 Gross D, Eisert J, Schuch N and Pérez-García D 2007 Phys. Rev. A 76 052315 [8] Lieb E, Schultz T and Mattis D 1961 Ann. Phys. 16 407 [9] Hastings M B 2004 Phys. Rev. B 69 104431 Nachtergaele B and Sims R 2007 Commun. Math. Phys. 276 437–72 [10] Oshikawa M, Yamanaka M and Affleck I 1997 Phys. Rev. Lett. 78 1984 [11] Pérez-García D, Wolf M M, Sanz M, Verstraete F and Cirac J I 2008 Phys. Rev. Lett. 100 167202 [12] Anfuso F and Rosch A 2007 Phys. Rev. B 76 085124 [13] Fannes M, Nachtergaele B and Werner R W 1992 Commun. Math. Phys. 144 443 [14] Pérez-García D, Verstraete F, Wolf M M and Cirac J I 2007 Quantum Inf. Comput. 7 401 [15] Vidal G 2003 Phys. Rev. Lett. 91 147902 [16] Schuch N, Wolf M M, Verstraete F and Cirac J I 2007 Phys. Rev. Lett. 98 140506 [17] Pérez-García D, Verstraete F, Cirac J I and Wolf M M 2008 Quantum. Inf. Comput. 8 0650–63 [18] Horn R A and Johnson C R 1991 Topics in Matrix Analysis (Cambridge: Cambridge University Press) [19] Singh S, Pfeifer R N C and Vidal G 2009 arXiv:0907.2994 [20] Sanz M, Wolf M M, Pérez-García D and Cirac J I 2009 Phys. Rev. A 79 042308 [21] Yu Kitaev A 2003 Ann. Phys. 303 2–30 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
Download
Original bundle
1 - 1 of 1
