LEADER 06165 am 22009373u 450 001 9910372747203321 005 20230126210518.0 010 $a3-030-34489-4 024 7 $a10.1007/978-3-030-34489-4 035 $a(CKB)4100000010121948 035 $a(DE-He213)978-3-030-34489-4 035 $a(MiAaPQ)EBC6112276 035 $a(Au-PeEL)EBL6112276 035 $a(OCoLC)1137851349 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/27404 035 $a(PPN)242844766 035 $a(EXLCZ)994100000010121948 100 $a20200127d2020 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTensor Network Contractions$b[electronic resource] $eMethods and Applications to Quantum Many-Body Systems /$fby Shi-Ju Ran, Emanuele Tirrito, Cheng Peng, Xi Chen, Luca Tagliacozzo, Gang Su, Maciej Lewenstein 205 $a1st ed. 2020. 210 $aCham$cSpringer Nature$d2020 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIV, 150 p. 68 illus., 65 illus. in color.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v964 311 $a3-030-34488-6 327 $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. 330 $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. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v964 606 $aPhysics 606 $aQuantum physics 606 $aQuantum optics 606 $aStatistical physics 606 $aMachine learning 606 $aElementary particles (Physics) 606 $aQuantum field theory 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aQuantum Optics$3https://scigraph.springernature.com/ontologies/product-market-codes/P24050 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aMachine Learning$3https://scigraph.springernature.com/ontologies/product-market-codes/I21010 606 $aElementary Particles, Quantum Field Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P23029 610 $aPhysics 610 $aQuantum physics 610 $aQuantum optics 610 $aStatistical physics 610 $aMachine learning 610 $aElementary particles (Physics) 610 $aQuantum field theory 615 0$aPhysics. 615 0$aQuantum physics. 615 0$aQuantum optics. 615 0$aStatistical physics. 615 0$aMachine learning. 615 0$aElementary particles (Physics). 615 0$aQuantum field theory. 615 14$aMathematical Methods in Physics. 615 24$aQuantum Physics. 615 24$aQuantum Optics. 615 24$aStatistical Physics and Dynamical Systems. 615 24$aMachine Learning. 615 24$aElementary Particles, Quantum Field Theory. 676 $a530.15 700 $aRan$b Shi-Ju$4aut$4http://id.loc.gov/vocabulary/relators/aut$0865967 702 $aTirrito$b Emanuele$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPeng$b Cheng$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aChen$b Xi$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTagliacozzo$b Luca$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSu$b Gang$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aLewenstein$b Maciej$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910372747203321 996 $aTensor Network Contractions$91932581 997 $aUNINA