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 re...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Xiang, Tao 1963- (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge ; New York, NY Cambridge University Press 2024
Schlagworte:	Renormalization group Tensor products Tensor algebra Density matrices Dichtematrix Tensorfeld Renormierungsgruppe
Online-Zugang:	DE-12 DE-634 DE-92 Volltext
Zusammenfassung:	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
Beschreibung:	Title from publisher's bibliographic system (viewed on 18 Jan 2024) Basic algebra of tensors -- Tensor network representation of classical statistical models -- Tensor network representation of operators -- Tensor network ansatz of wave functions -- Criterion of truncation : symmetric systems -- Real-space DMRG -- Implementation of symmetries -- DMRG with nonlocal basis states -- Matrix product states -- Infinite matrix product states -- Determination of MPS -- Continuous matrix product states -- Classical transfer matrix renormalization -- Criterion of truncation : nonsymmetric systems -- Renormalization of quantum transfer matrices -- MPS solution of QTMRG -- Time-dependent methods -- Tangent-space approaches -- Tree tensor network states -- Two-dimensional tensor network states -- Coarse-graining tensor renormalization
Beschreibung:	1 Online-Ressource (xx, 433 Seiten)
ISBN:	9781009398671
DOI:	10.1017/9781009398671