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100 1 _aRan, Shi-Ju.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTensor Network Contractions
_h[electronic resource] :
_bMethods and Applications to Quantum Many-Body Systems /
_cby Shi-Ju Ran, Emanuele Tirrito, Cheng Peng, Xi Chen, Luca Tagliacozzo, Gang Su, Maciej Lewenstein.
250 _a1st ed. 2020.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2020.
300 _aXIV, 150 p. 68 illus., 65 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
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347 _atext file
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490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v964
505 0 _aIntroduction -- Tensor Network: Basic Definitions and Properties -- Two-Dimensional Tensor Networks and Contraction Algorithms -- Tensor Network Approaches for Higher-Dimensional Quantum Lattice Models -- Tensor Network Contraction and Multi-Linear Algebra -- Quantum Entanglement Simulation Inspired by Tensor Network -- Summary.
506 0 _aOpen Access
520 _aTensor 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.
650 0 _aPhysics.
650 0 _aQuantum physics.
650 0 _aQuantum optics.
650 0 _aStatistical physics.
650 0 _aMachine learning.
650 0 _aElementary particles (Physics).
650 0 _aQuantum field theory.
650 1 4 _aMathematical Methods in Physics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P19013
650 2 4 _aQuantum Physics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P19080
650 2 4 _aQuantum Optics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P24050
650 2 4 _aStatistical Physics and Dynamical Systems.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P19090
650 2 4 _aMachine Learning.
_0https://scigraph.springernature.com/ontologies/product-market-codes/I21010
650 2 4 _aElementary Particles, Quantum Field Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/P23029
700 1 _aTirrito, Emanuele.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aPeng, Cheng.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aChen, Xi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aTagliacozzo, Luca.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aSu, Gang.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aLewenstein, Maciej.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030344887
776 0 8 _iPrinted edition:
_z9783030344900
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v964
856 4 0 _uhttps://doi.org/10.1007/978-3-030-34489-4
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