Density Matrix and Tensor Network Renormalization

An introduction to tensor network renormalization, a powerful tool for the study of quantum many-body problems and complex systems.

This book provides a comprehensive introduction to the theory of tensor network renormalization for the first time. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.Renormalization group theory of tensor network states provides a powerful tool for studying quantum many-body problems and a new paradigm for understanding entangled structures of complex systems. In recent decades the theory has rapidly evolved into a universal framework and language employed by researchers in fields ranging from condensed matter theory to machine learning. This book presents a pedagogical and comprehensive introduction to this field for the first time. After an introductory survey on the major advances in tensor network algorithms and their applications, it introduces step-by-step the tensor network representations of quantum states and the tensor-network renormalization group methods developed over the past three decades. Basic statistical and condensed matter physics models are used to demonstrate how the tensor network renormalization works. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.