Matrix product states with long-range localizable entanglement
| dc.contributor.author | Wahl, T. B. | |
| dc.contributor.author | Pérez García, David | |
| dc.contributor.author | Cirac, Juan I. | |
| dc.date.accessioned | 2023-06-20T00:22:11Z | |
| dc.date.available | 2023-06-20T00:22:11Z | |
| dc.date.issued | 2012-12 | |
| dc.description.abstract | We derive a criterion to determine when a translationally invariant matrix product state (MPS) has long-range localizable entanglement, where that quantity remains finite in the thermodynamic limit. We give examples fulfilling this criterion and eventually use it to obtain all such MPS with bond dimension 2 and 3. | |
| 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 | Unión Europea. FP7 | |
| dc.description.sponsorship | Comunidad de Madrid | |
| dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17609 | |
| dc.identifier.doi | 10.1103/PhysRevA.86.062314 | |
| dc.identifier.issn | 1050-2947 | |
| dc.identifier.officialurl | http://link.aps.org/doi/10.1103/PhysRevA.86.062314 | |
| dc.identifier.relatedurl | http://arxiv.org/abs/1206.4254 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42466 | |
| dc.issue.number | 6 | |
| dc.journal.title | Physical Review A | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | QUEVADIS (233859) | |
| dc.relation.projectID | QUITEMAD-CM (S2009/ESP-1594) | |
| dc.relation.projectID | AQUTE | |
| dc.relation.projectID | CHIST-ERA Project CQC | |
| dc.relation.projectID | (MTM2011-26912) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Local operations | |
| dc.subject.keyword | Spin chains | |
| dc.subject.keyword | Field | |
| dc.subject.ucm | Física matemática | |
| dc.title | Matrix product states with long-range localizable entanglement | |
| dc.type | journal article | |
| dc.volume.number | 86 | |
| dcterms.references | F. Verstraete, M. Popp, and J. I. Cirac, Phys. Rev. Lett. 92, 027901 (2004). H.-J. Briegel, W. D�ur, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 81, 5932 (1998). F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. 92, 087201 (2004). R. Orus, and H.-H. Tu, Phys. Rev. B 83, 201101(R) (2011); S. O. Skrvseth, and S. D. Bartlett, Phys. Rev. A 80, 022316 (2009); J. K. Pachos, and M. B. Plenio, Phys. Rev. Lett. 93, 056402 (2004); B.-Q. Jin, and V. E. Korepin, Phys. Rev. A 69, 062314 (2004). J. Fiurasek, and L. Mi sta, Jr., Phys. Rev. A 75, 060302(R) (2007); A. Serani, G. Adesso, and F. Illuminati, Phys. Rev. A 71, 032349 (2005); G. Adesso, and F. Illuminati, Phys. Rev. Lett. 95, 150503 (2005). V. Subrahmanyama, and A. Lakshminarayanb, Phys. Lett. A 349, 164 (2006). L. Campos Venuti, and M. Roncaglia, Phys. Rev. Lett. 94, 207207 (2005); S. Sahoo, arXiv:1201.5620v4. The case of LRLE needs to be differentiated from the one of diverging entanglement length introduced in [1]: A divergence of the entanglement length only implies that the LE cannot decay exponentially with the spin distance, however it still may decay algebraically, c.f. [12]. D. Perez-Garca, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quant. Inf. Comp. 7, 401 (2007). C. Schon, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, Phys. Rev. Lett. 95, 110503 (2005). M. Fannes, B. Nachtergaele, R. F. Werner, Commun. Math. Phys. 144, 443 (1992). M. Popp, F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. A 71, 042306 (2005). O. F. Sylju asen, Phys. Lett. A 322, 25 (2004); M. Popp, F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Appl. Phys. B 82, 225 (2006); P. Androvitsaneas, E. Paspalakis, and A. F. Terzis, Ann. Phys. 327, 212 (2012). W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998). F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. 92, 087201 (2004). Note that for D = 2 all isometries are unitaries, i.e., according to (11) all matrices Ai have to be proportional to unitaries themselves. H. Hironaka, Ann. Math. 79, 109 (1964); B. Buchberger, Austria, Universitat Innsbruck, Diss., 1965. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A 53, 2046 (1996). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
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