Sequentially generated states for the study of two-dimensional systems
| dc.contributor.author | Bañuls, M.C. | |
| dc.contributor.author | Pérez García, David | |
| dc.contributor.author | Wolf, M.M. | |
| dc.contributor.author | Verstraete, F. | |
| dc.contributor.author | Cirac, J.I. | |
| dc.date.accessioned | 2023-06-20T09:45:29Z | |
| dc.date.available | 2023-06-20T09:45:29Z | |
| dc.date.issued | 2008 | |
| dc.description.abstract | Matrix product states can be defined as the family of quantum states that can be sequentially generated in a one-dimensional system [Schon et al., Phys. Rev. Lett. 95, 110503 (2005)]. We introduce a family of states that extends this definition to two dimensions. Like in matrix product states, expectation values of few body observables can be efficiently evaluated and, for the case of translationally invariant systems, the correlation functions decay exponentially with the distance. We show that such states are a subclass of projected entangled pair states and investigate their suitability for approximating the ground states of local Hamiltonians. | |
| 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 | EU Strep Compas | |
| dc.description.sponsorship | DFG | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17824 | |
| dc.identifier.doi | http//dx.doi.org/10.1103/PhysRevA.77.052306 | |
| dc.identifier.issn | 1050-2947 | |
| dc.identifier.officialurl | http://link.aps.org/doi/10.1103/PhysRevA.77.052306 | |
| dc.identifier.relatedurl | http://www.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50311 | |
| dc.journal.title | Physical Review A | |
| dc.language.iso | eng | |
| dc.page.final | 1 | |
| dc.page.initial | 052306 | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | (MTM2005-00082) | |
| dc.relation.projectID | Excellence Cluster MAP | |
| dc.relation.projectID | FOR 635 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 530.145 | |
| dc.subject.ucm | Teoría de los quanta | |
| dc.subject.unesco | 2210.23 Teoría Cuántica | |
| dc.title | Sequentially generated states for the study of two-dimensional systems | |
| dc.type | journal article | |
| dc.volume.number | 77 | |
| dcterms.references | S. R. White, Phys. Rev. Lett. 69, 2863 (1992) D. Perez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, Quantum Inf. Comput. 7, 401 (2007). G. Vidal, Phys. Rev. Lett. 91, 147902 (2003). F. Verstraete and J. I. Cirac, e-print arXiv:cond-mat/0407066. C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, Phys. Rev. Lett. 95, 110503 (2005). N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 98, 140506 (2007). V. Murg, F. Verstraete, and J. I. Cirac, Phys. Rev. A 75, 033605 (2007). J. Jordan, R. Orús, G. Vidal, F. Verstraete, and J. I. Cirac, e-print arXiv:cond-mat/0703788v3. G. Vidal, Phys. Rev. Lett. 99, 220405 (2007). S. Anders, M. B. Plenio, W. Dür, F. Verstraete, and H.-J. Briegel, Phys. Rev. Lett. 97, 107206 (2006). S. Moukouri, Phys. Rev. B 70, 014403 (2004). N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, Phys. Rev. Lett. 100, 040501 (2008). C. M. Dawson, J. Eisert, and T. J. Osborne, Phys. Rev. Lett. 100, 130501 (2008). M. B. Hastings, Phys. Rev. B 76, 201102(R) (2007). U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005). F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004). F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004). F. Verstraete, M. M. Wolf, D. Perez-García, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006). F. Verstraete and J. I. Cirac, Phys. Rev. A 70, 060302(R) (2004). D. Pérez-García, F. Verstraete, J. I. Cirac, and M. M. Wolf, e-print arXiv:0707.2260v1. H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001). The scaling depends exponentially on the number of local operators applied, so that the calculation is feasible as long as this number is small. V. Murg (private communication). MPSs have bond dimension D, and unitaries act on M+1 sites, so that dM=D. G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003). M. B. Hastings, Phys. Rev. B 73, 085115 (2006). M. B. Hastings, Phys. Rev. B 76, 035114 (2007). J. Eisert, Phys. Rev. Lett. 97, 260501 (2006). A. Y. Kitaev, Ann. Phys. 303, 2 (2003). | |
| 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
