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    Tensor Network Contractions

    Methods and Applications to Quantum Many-Body Systems

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    Author(s)
    Ran, Shi-Ju
    Tirrito, Emanuele
    Peng, Cheng
    Chen, Xi
    Tagliacozzo, Luca
    Su, Gang
    Lewenstein, Maciej
    Language
    English
    Show full item record
    Abstract
    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.
    URI
    http://library.oapen.org/handle/20.500.12657/23120
    Keywords
    Physics; Physics; Quantum physics; Quantum optics; Statistical physics; Machine learning; Elementary particles (Physics); Quantum field theory
    DOI
    10.1007/978-3-030-34489-4
    Publisher
    Springer Nature
    Publisher website
    https://www.springernature.com/gp/products/books
    Publication date and place
    Cham, 2020
    Series
    Lecture Notes in Physics,
    Classification
    Optical physics
    Quantum physics (quantum mechanics and quantum field theory)
    Statistical physics
    Mathematical physics
    Machine learning
    Pages
    150
    Rights
    https://creativecommons.org/licenses/by/4.0
    • Imported or submitted locally

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    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

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