密度矩陣與張量網絡重正化=Density Matrix and Tensor Network Renormalizati
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物品所在地：中國大陸
原出版社：北京大學
物品所在地：中國大陸
原出版社：北京大學
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202409*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：密度矩陣與張量網絡重正化=Density Matrix and Tensor Network Renormalization ISBN：9787301353875 出版社：北京大學 著編譯者：向濤 叢書名：中外物理學精品書系 頁數：439 所在地：中國大陸 *此為代購商品 書號：1684063 可大量預訂，請先連絡。 【台灣高等教育出版社簡體書】 密度矩陣與張量網絡重正化=Density Matrix and Tensor Network Renormalization 787301353875 向濤 內容簡介 本書介紹了過去三十年發展起來的張量網路態重正化群理論。本書首先介紹了張量網路態的分解和取值所需的張量代數基礎。之後，本書又介紹了量子態的張量網路表示、量子運算元、配分函數（例如矩陣乘積態）、投影糾纏對態等。 接下來，本書又介紹了密度矩陣重正化群（DMRG）及其各種拓展，比如動量空間DMRG、經典或量子躍遷矩陣重整化群方法、時間依賴DMRG、動力學DMRG等。 本書適合凝聚態物理，特別是張量網路態領域的科研工作者參考，也可用於初入此研究方向的青年學者學習。作者簡介 向濤，中國科學院物理研究所研究員，中國科學院院士、發展中國家科學院院士。1984年本科畢業於清華大學，1986年在清華大學獲得碩士學位，1990年在中國科學院理論物理研究所獲得博士學位。《中國物理快報》主編。從事凝聚態物理，特別是強關聯量子問題的理論研究。目錄 ContentsPreface Unit Used Notations and Graphical Representations List of Abbreviations 1 Introduction 1 1 Quantum Many-Body Problems 1 2 From NRG to DMRG 1 3 From DMRG to Tensor Network Algorithms 1 4 Applications 2 Basic Algebra of Tensors 2 1 Diagrammatic Representation of Tensors 2 2 QR and LQ Decompositions 2 3 LU Decomposition with Partial Pivoting 2 4 Singular Value Decomposition 2 5 Polar Decomposition 2 6 Higher-Order Singular Value Decomposition 2 7 Low-Rank Approximation of Tensors 2 8 Automatic Differentiation 2 9 Trotter-Suzuki Decomposition 3 Tensor Network Representation of Classical Statistical Models 3 1 Tensor Network Models 3 2 Matrix-Network Models 3 3 Tensor Network Representation in the Original Lattice 3 4 Tensor Network Representation in the Dual Space 3 5 Vertex-Sharing Lattice Models 3 6 Duality Properties of Tensor Network Models 4 Tensor Network Representation of Operators 4 1 Matrix Product Operators (MPO) 4 2 Imaginary Time Evolution Operato 4 3 Quantum Transfer Matrix 4 4 MPO Representation of Quantum Transfer Matrix 5 Tensor Network Ansatz ofWave Functions 5 1 Area Law of Entanglement Entropy 5 2 Matrix Product States (MPS) 5 3 One-Dimensional AKLT States 5 4 Multiscale Entanglement Renormalization Ansatz (MERA) 5 5 Projected Entangled Pair State (PEPS) 5 6 Projected Entangled Simplex State (PESS) 6 Criterion of Truncation: Symmetric Systems 6 1 Density Matrix 6 2 Reduced Density Matrix 6 3 Schmidt Decomposition 6 4 Variational Approach 6 5 Edge and Bond Density Matrices 7 Real-Space DMRG 7 1 Two Kinds of Algorithms 7 2 DMRG in the MPO Language 7 3 Error Analysis 7 4 Heisenberg Spin Chains 7 5 Periodic System 7 6 Multiple Target States 7 7 Two-Dimensional Systems 8 Implementation of Symmetries 8 1 Symmetry Consideration 8 2 Continuous Abelian Symmetries 8 3 Spin Reflection Symmetry 8 4 Spatial Reflection Symmetry 8 5 Non-Abelian Symmetries 9 DMRG with Nonlocal Basis States 9 1 General Consideration 9 2 Momentum-Space DMRG 9 3 DMRG in a General Basis Space 9 4 Optimization of Single-Particle Basis States 9 5 Optimizing Active Basis Space 10 Matrix Product States 10 1 The DMRG Wave Function 10 2 Canonical Representations 10 3 Canonical Transformation 10 4 Implementation of Symmetries 11 Infinite Matrix Product States 11 1 Translation Invariant MPS 11 2 Transfer Matrix and Canonical Transformation 11 3 Expectation Values of Physical Observables 11 4 String Order Parameter 11 5 MPS with a Finite Unit Cell 12 Determination of MPS 12 1 Variational Optimization 12 2 Excited states 12 3 Imaginary Time Evolution 12 4 Purification 13 Continuous Matrix Product States 13 1 Lattice Discretization of Continuous Quantum Field Theory 13 2 Continuum limit of MPS 13 3 Expectation Values 13 4 Canonicalization 13 5 Determination of Continuous MPS 14 Classical Transfer Matrix Renormalization 14 1 Classical Transfer Matrix 14 2 TMRG 14 3 Fixed-Point MPS: One-site Approach 14 4 Fixed-Point MPS: Two-Site Approach 14 5 Corner Transfer Matrix Renormalization 15 Criterion of Truncation: Nonsymmetric Systems 15 1 Nonsymmetric Density Matrix 15 2 Transformation Matrices 15 3 Canonicalization of the Transformation Matrices 15 4 Biorthonormalization 15 5 Low-Rank Approximation to the Environment Density Matrix 16 Renormalization of Quantum Transfer Matrices 16 1 Quantum Transfer Matrix and Thermodynamics 16 2 Correlation Functions 16 3 QTMRG 16 4 Thermodynamics of the Heisenberg Spin Chain 17 MPS Solution of QTMRG 17 1 Biorthonormal MPS 17 2 Biorthonormalization 17 3 Fixed-Point Equations 17 4 Translation Invariant System with a Finite Unit Cell 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
