Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems

Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic...

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Autores:
Tipo de recurso:
Book
Fecha de publicación:
2020
Institución:
Universidad de Bogotá Jorge Tadeo Lozano
Repositorio:
Expeditio: repositorio UTadeo
Idioma:
eng
OAI Identifier:
oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/18480
Acceso en línea:
https://directory.doabooks.org/handle/20.500.12854/27404
http://hdl.handle.net/20.500.12010/18480
Palabra clave:
Physics
Quantum physics
Quantum optics
Análisis funcional
Caos cuántico
Teoría cuántica
Rights
License
Abierto (Texto Completo)
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oai_identifier_str oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/18480
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dc.title.spa.fl_str_mv Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
title Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
spellingShingle Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
Physics
Quantum physics
Quantum optics
Análisis funcional
Caos cuántico
Teoría cuántica
title_short Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
title_full Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
title_fullStr Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
title_full_unstemmed Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
title_sort Tensor Network Contractions : Methods and Applications to Quantum Many-Body Systems
dc.subject.spa.fl_str_mv Physics
Quantum physics
Quantum optics
topic Physics
Quantum physics
Quantum optics
Análisis funcional
Caos cuántico
Teoría cuántica
dc.subject.lemb.spa.fl_str_mv Análisis funcional
Caos cuántico
Teoría cuántica
description Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
publishDate 2020
dc.date.created.none.fl_str_mv 2020
dc.date.accessioned.none.fl_str_mv 2021-04-05T19:20:53Z
dc.date.available.none.fl_str_mv 2021-04-05T19:20:53Z
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_2f33
format http://purl.org/coar/resource_type/c_2f33
dc.identifier.isbn.none.fl_str_mv 978-3-030-34489-4
dc.identifier.other.none.fl_str_mv https://directory.doabooks.org/handle/20.500.12854/27404
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/20.500.12010/18480
dc.identifier.doi.none.fl_str_mv 10.1007/978-3-030-34489-4
identifier_str_mv 978-3-030-34489-4
10.1007/978-3-030-34489-4
url https://directory.doabooks.org/handle/20.500.12854/27404
http://hdl.handle.net/20.500.12010/18480
dc.language.iso.spa.fl_str_mv eng
language eng
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.local.spa.fl_str_mv Abierto (Texto Completo)
dc.rights.creativecommons.none.fl_str_mv https://creativecommons.org/licenses/by/4.0
rights_invalid_str_mv Abierto (Texto Completo)
https://creativecommons.org/licenses/by/4.0
http://purl.org/coar/access_right/c_abf2
dc.format.extent.spa.fl_str_mv 150 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Springer Nature
institution Universidad de Bogotá Jorge Tadeo Lozano
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spelling 2021-04-05T19:20:53Z2021-04-05T19:20:53Z2020978-3-030-34489-4https://directory.doabooks.org/handle/20.500.12854/27404http://hdl.handle.net/20.500.12010/1848010.1007/978-3-030-34489-4Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.150 páginasapplication/pdfengSpringer NaturePhysicsQuantum physicsQuantum opticsAnálisis funcionalCaos cuánticoTeoría cuánticaTensor Network Contractions : Methods and Applications to Quantum Many-Body SystemsAbierto (Texto Completo)https://creativecommons.org/licenses/by/4.0http://purl.org/coar/access_right/c_abf2http://purl.org/coar/resource_type/c_2f33Ran, Shi-JuTirrito, EmanuelePeng, ChengChen, XiTagliacozzo, LucaSu, GangLewenstein, MaciejORIGINAL1007036.pdf1007036.pdfVer documentoapplication/pdf4739100https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/18480/1/1007036.pdf3b7887d435883f15024328ce71439c82MD51open accessTHUMBNAIL1007036.pdf.jpg1007036.pdf.jpgIM Thumbnailimage/jpeg15531https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/18480/3/1007036.pdf.jpg9c264d5f4c2689b8902e0902e618bae4MD53open accessLICENSElicense.txtlicense.txttext/plain; charset=utf-82938https://expeditiorepositorio.utadeo.edu.co/bitstream/20.500.12010/18480/2/license.txtbaba314677a6b940f072575a13bb6906MD52open access20.500.12010/18480oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/184802021-04-05 23:01:56.84open accessRepositorio Institucional - Universidad Jorge Tadeo Lozanoexpeditio@utadeo.edu.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