Introduction to tensor network methods : numerical simulations of low-dimensional many-body quantum systems /: numerical simulations of low-dimensional many-body quantum systems. ([2018])

• Record Type: Book
• Further Information: Note: Simone Montangero.
• Authors: Montangero, Simone
• Contents: Intro; Preface; Contents; Symbols and Abbreviations; 1 Introduction; Part I The Single Body Problem; 2 Linear Algebra; 2.1 System of Linear Equations; 2.1.1 LU Reduction; 2.2 Eigenvalue Problem; 2.2.1 Power Methods; 2.3 Tridiagonal Matrices; 2.4 Lanczos Methods; 2.5 Exercises; 3 Numerical Calculus; 3.1 Classical Quadrature; 3.2 Gaussian Integration; 3.3 Time-Independent Schrödinger Equation; 3.3.1 Finite Difference Method; 3.3.2 Variational Method; 3.4 Time-Dependent Schrödinger Equation; 3.4.1 Spectral Method; 3.4.2 Split Operator Method; 3.4.3 Partial Differential Equations Solvers 3.5 ExercisesPart II The Many-Body Problem; 4 Numerical Renormalization Group Methods; 4.1 Mean Field Theory; 4.1.1 Quantum Ising Model in Transverse Field; 4.1.2 Cluster Mean Field; 4.2 Real-Space Renormalization Group; 4.3 Density Matrix Renormalization Group; 4.4 Exercises; 5 Tensor Network Methods; 5.1 Tensor Definition; 5.2 Tensor Manipulations; 5.2.1 Index Fusion and Splitting; 5.2.2 Compression; 5.2.3 Tensor Network Differentiation; 5.2.4 Gauging; 5.2.5 Tensor Contraction Complexity; 5.3 Ground States via Tensor Networks; 5.3.1 Mean Field; 5.3.2 Graphical Tensor Notation 5.3.3 Matrix Product States5.3.4 Loop-Free Tensor Networks; 5.3.5 Looped Tensor Networks; 5.4 Time Evolution via Tensor Networks; 5.4.1 Time-Dependent Density Matrix Renormalization Group; 5.4.2 Fidelity-Driven Evolution; 5.4.3 Time-Dependent Variational Principle; 5.5 Measurements; 5.6 Further Developments; 5.7 Software; 5.8 Exercises; 6 Symmetric Tensor Networks; 6.1 Elements of Group Theory; 6.2 Global Pointlike Symmetries; 6.3 Quantum Link Formulation of Gauge Symmetries; 6.4 Lattice Gauge Invariant Tensor Networks; 6.5 Exercises; Part III Applications 7 Many-Body Quantum Systems at Equilibrium7.1 Phase Transitions; 7.2 Quantum-Classical Statistical Correspondence; 7.3 Quantum Phase Transition; 7.3.1 Critical Exponents; 7.4 Entanglement Measures; 7.4.1 Central Charge; 7.4.2 Topological Entanglement Entropy; 7.5 Exercises; 8 Out-of-Equilibrium Processes; 8.1 Adiabatic Quantum Computation; 8.1.1 Adiabatic Theorem; 8.1.2 Applications; 8.2 Kibble-Zurek Mechanism; 8.2.1 Crossover from Quantum to Classical Kibble-Zurek; 8.3 Optimal Control of Many-Body Quantum Systems; 8.4 Other Applications; 8.5 Exercises; A Hardware in a Nutshell for Physicists A.1 ArchitectureA.2 Data and Formats; A.3 Memory and Data Processing; A.4 Multiprocessors; A.5 Exercises; B Software in a Nutshell for Physicists; B.1 Correctness; B.2 Numerical Stability; B.3 Accurate Discretization; B.4 Flexibility; B.5 Efficiency; B.6 Exercises; References; ; Index
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 512/.57; Tensor fields; MATHEMATICS / Algebra / Intermediate; Numerical and Computational Physics, Simulation; Quantum Physics; Quantum Computing; Mathematical Applications in the Physical Sciences; Tensor fields; Electronic books
• Languages: English
• ISBNs: 9783030014094; 3030014096
• Related ISBNs: 9783030014087
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (EBSCO, viewed December 4, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.