Density matrix and tensor network renormalization:
Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by re...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York, NY
Cambridge University Press
2024
|
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-634 DE-92 Volltext |
| Zusammenfassung: | Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 18 Jan 2024) Basic algebra of tensors -- Tensor network representation of classical statistical models -- Tensor network representation of operators -- Tensor network ansatz of wave functions -- Criterion of truncation : symmetric systems -- Real-space DMRG -- Implementation of symmetries -- DMRG with nonlocal basis states -- Matrix product states -- Infinite matrix product states -- Determination of MPS -- Continuous matrix product states -- Classical transfer matrix renormalization -- Criterion of truncation : nonsymmetric systems -- Renormalization of quantum transfer matrices -- MPS solution of QTMRG -- Time-dependent methods -- Tangent-space approaches -- Tree tensor network states -- Two-dimensional tensor network states -- Coarse-graining tensor renormalization |
| Beschreibung: | 1 Online-Ressource (xx, 433 Seiten) |
| ISBN: | 9781009398671 |
| DOI: | 10.1017/9781009398671 |
Internformat
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| 500 | |a Basic algebra of tensors -- Tensor network representation of classical statistical models -- Tensor network representation of operators -- Tensor network ansatz of wave functions -- Criterion of truncation : symmetric systems -- Real-space DMRG -- Implementation of symmetries -- DMRG with nonlocal basis states -- Matrix product states -- Infinite matrix product states -- Determination of MPS -- Continuous matrix product states -- Classical transfer matrix renormalization -- Criterion of truncation : nonsymmetric systems -- Renormalization of quantum transfer matrices -- MPS solution of QTMRG -- Time-dependent methods -- Tangent-space approaches -- Tree tensor network states -- Two-dimensional tensor network states -- Coarse-graining tensor renormalization | ||
| 520 | |a Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area | ||
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Datensatz im Suchindex
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| author | Xiang, Tao 1963- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/9781009398671 |
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| id | DE-604.BV049661017 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-05T17:01:40Z |
| institution | BVB |
| isbn | 9781009398671 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035004254 |
| oclc_num | 1437851642 |
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| owner_facet | DE-12 DE-92 DE-634 |
| physical | 1 Online-Ressource (xx, 433 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO BTU_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 2024 |
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| publisher | Cambridge University Press |
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| spelling | Xiang, Tao 1963- (DE-588)1261916867 aut Density matrix and tensor network renormalization Tao Xiang Cambridge ; New York, NY Cambridge University Press 2024 1 Online-Ressource (xx, 433 Seiten) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 18 Jan 2024) Basic algebra of tensors -- Tensor network representation of classical statistical models -- Tensor network representation of operators -- Tensor network ansatz of wave functions -- Criterion of truncation : symmetric systems -- Real-space DMRG -- Implementation of symmetries -- DMRG with nonlocal basis states -- Matrix product states -- Infinite matrix product states -- Determination of MPS -- Continuous matrix product states -- Classical transfer matrix renormalization -- Criterion of truncation : nonsymmetric systems -- Renormalization of quantum transfer matrices -- MPS solution of QTMRG -- Time-dependent methods -- Tangent-space approaches -- Tree tensor network states -- Two-dimensional tensor network states -- Coarse-graining tensor renormalization Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area Renormalization group Tensor products Tensor algebra Density matrices Dichtematrix (DE-588)4149624-3 gnd rswk-swf Tensorfeld (DE-588)4202754-8 gnd rswk-swf Renormierungsgruppe (DE-588)4177773-6 gnd rswk-swf Tensorfeld (DE-588)4202754-8 s Dichtematrix (DE-588)4149624-3 s Renormierungsgruppe (DE-588)4177773-6 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-009-39870-1 https://doi.org/10.1017/9781009398671 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Xiang, Tao 1963- Density matrix and tensor network renormalization Renormalization group Tensor products Tensor algebra Density matrices Dichtematrix (DE-588)4149624-3 gnd Tensorfeld (DE-588)4202754-8 gnd Renormierungsgruppe (DE-588)4177773-6 gnd |
| subject_GND | (DE-588)4149624-3 (DE-588)4202754-8 (DE-588)4177773-6 |
| title | Density matrix and tensor network renormalization |
| title_auth | Density matrix and tensor network renormalization |
| title_exact_search | Density matrix and tensor network renormalization |
| title_full | Density matrix and tensor network renormalization Tao Xiang |
| title_fullStr | Density matrix and tensor network renormalization Tao Xiang |
| title_full_unstemmed | Density matrix and tensor network renormalization Tao Xiang |
| title_short | Density matrix and tensor network renormalization |
| title_sort | density matrix and tensor network renormalization |
| topic | Renormalization group Tensor products Tensor algebra Density matrices Dichtematrix (DE-588)4149624-3 gnd Tensorfeld (DE-588)4202754-8 gnd Renormierungsgruppe (DE-588)4177773-6 gnd |
| topic_facet | Renormalization group Tensor products Tensor algebra Density matrices Dichtematrix Tensorfeld Renormierungsgruppe |
| url | https://doi.org/10.1017/9781009398671 |
| work_keys_str_mv | AT xiangtao densitymatrixandtensornetworkrenormalization |