Frustration Free Gapless Hamiltonians for Matrix Product States
| dc.contributor.author | Fernández González, C. | |
| dc.contributor.author | Schuch, N. | |
| dc.contributor.author | Wolf, M.M. | |
| dc.contributor.author | Cirac, J.I. | |
| dc.contributor.author | Pérez García, David | |
| dc.date.accessioned | 2023-06-19T13:27:54Z | |
| dc.date.available | 2023-06-19T13:27:54Z | |
| dc.date.issued | 2015-01 | |
| dc.description.abstract | For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state space (the so-called non-injective case), we construct another ’uncle’ Hamiltonian which is also local and frustration free, has the same ground state space, but is gapless, and its spectrum is R +. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Comunidad de Madrid | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.sponsorship | European CHIST-ERA | |
| dc.description.sponsorship | Unión Europea. FP7 | |
| dc.description.sponsorship | NSF | |
| dc.description.sponsorship | ARO | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/28340 | |
| dc.identifier.doi | 10.1007/s00220-014-2173-z | |
| dc.identifier.issn | 0010-3616 | |
| dc.identifier.officialurl | http://link.springer.com/article/10.1007%2Fs00220-014-2173-z | |
| dc.identifier.relatedurl | http://link.springer.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33778 | |
| dc.issue.number | 1 | |
| dc.journal.title | Communications in Mathematical Physics | |
| dc.language.iso | eng | |
| dc.page.final | 333 | |
| dc.page.initial | 299 | |
| dc.publisher | Springer | |
| dc.relation.projectID | QUITEMAD-CM (S2009/ESP-1594) | |
| dc.relation.projectID | (MTM2011-26912) | |
| dc.relation.projectID | (CQC) | |
| dc.relation.projectID | QUEVADIS | |
| dc.relation.projectID | (PHY-0803371) | |
| dc.relation.projectID | (W911NF-09-1-0442) | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 530.1 | |
| dc.subject.keyword | Spin chains | |
| dc.subject.keyword | Quantum | |
| dc.subject.ucm | Física matemática | |
| dc.subject.ucm | Teoría de los quanta | |
| dc.subject.unesco | 2210.23 Teoría Cuántica | |
| dc.title | Frustration Free Gapless Hamiltonians for Matrix Product States | |
| dc.type | journal article | |
| dc.volume.number | 333 | |
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| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5edb2da8-669b-42d1-867d-8fe3144eb216 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
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