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.
