Density Matrix and Tensor Network Renormalization / Tao Xiang.

Format:

Book

Author/Creator:

Xiang, Tao (Physics professor), author.

Language:

English

Subjects (All):

Renormalization group.

Density matrices.

Quantum theory.

Tensor algebra.

Tensor fields.

Tensor products.

Physical Description:

1 online resource (xx, 433 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge, England : Cambridge University Press, [2023]

Summary:

"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"-- Provided by publisher

Contents:

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

Notes:

Title from publisher's bibliographic system (viewed on 18 Jan 2024).

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9781009398718

1009398717

9781009398671

1009398679