Tensor Network Contractions : Methods and Applications to Quantum ManyBody Systems
 Responsibility
 ShiJu Ran, Emanuele Tirrito, Cheng Peng, Xi Chen, Luca Tagliacozzo, Gang Su, Maciej Lewenstein.
 Publication
 Cham : Springer, 2020.
 Physical description
 1 online resource (xiv, 150 pages) : illustrations (some color)
 Series
 Lecture notes in physics ; v. 964.
Online
More options
Description
Creators/Contributors
 Author/Creator
 Ran, ShiJu.
 Contributor
 Tirrito, Emanuele.
 Peng, Cheng.
 Chen, Xi.
 Tagliacozzo, Luca.
 Su, Gang.
 Lewenstein, Maciej.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introduction
 Tensor Network: Basic Definitions and Properties
 TwoDimensional Tensor Networks and Contraction Algorithms
 Tensor Network Approaches for HigherDimensional Quantum Lattice Models
 Tensor Network Contraction and MultiLinear Algebra
 Quantum Entanglement Simulation Inspired by Tensor Network
 Summary.
 Summary
 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 bigdata 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 manybody 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 nonspecialists on quantum physics to understand tensor network algorithms and the related mathematics.
Subjects
 Subjects
 Manybody problem.
 Physics > Textbooks.
 Tensor algebra.
 Quantum theory.
 Quantum optics.
 Statistical physics.
 Machine learning.
 Particles (Nuclear physics)
 Quantum field theory.
 Quantum Theory
 Elementary Particles
 Problème des N corps.
 Algèbre tensorielle.
 Théorie quantique.
 Optique quantique.
 Physique statistique.
 Apprentissage automatique.
 Particules (Physique nucléaire)
 Théorie quantique des champs.
 particle physics.
 Quantum physics (quantum mechanics & quantum field theory)
 Optical physics.
 Mathematical physics.
 Science > Quantum Theory.
 Science > Optics.
 Science > Mathematical Physics.
 Computers > Intelligence (AI) & Semantics.
 Science > Nuclear Physics.
 Physics.
Bibliographic information
 Publication date
 2020
 Series
 Lecture notes in physics ; v. 964
 ISBN
 9783030344894
 3030344894
 9783030344887 (print)