Book contents
- Frontmatter
- Contents
- Preface
- Unit Used
- Notations and Graphical Representations
- Abbreviations
- 1 Introduction
- 2 Basic Algebra of Tensors
- 3 Tensor Network Representation of Classical Statistical Models
- 4 Tensor Network Representation of Operators
- 5 Tensor Network Ansatz of Wave Functions
- 6 Criterion of Truncation: Symmetric Systems
- 7 Real-Space DMRG
- 8 Implementation of Symmetries
- 9 DMRG with Nonlocal Basis States
- 10 Matrix Product States
- 11 Infinite Matrix Product States
- 12 Determination of MPS
- 13 Continuous Matrix Product States
- 14 Classical Transfer Matrix Renormalization
- 15 Criterion of Truncation: Nonsymmetric Systems
- 16 Renormalization of Quantum Transfer Matrices
- 17 MPS Solution of QTMRG
- 18 Dynamical Correlation Functions
- 19 Time-Dependent Methods
- 20 Tangent-Space Approaches
- 21 Tree Tensor Network States
- 22 Two-Dimensional Tensor Network States
- 23 Coarse-Graining Tensor Renormalization
- Appendix Other Numerical Methods
- References
- Index
7 - Real-Space DMRG
Published online by Cambridge University Press: 18 January 2024
Book contents
- Frontmatter
- Contents
- Preface
- Unit Used
- Notations and Graphical Representations
- Abbreviations
- 1 Introduction
- 2 Basic Algebra of Tensors
- 3 Tensor Network Representation of Classical Statistical Models
- 4 Tensor Network Representation of Operators
- 5 Tensor Network Ansatz of Wave Functions
- 6 Criterion of Truncation: Symmetric Systems
- 7 Real-Space DMRG
- 8 Implementation of Symmetries
- 9 DMRG with Nonlocal Basis States
- 10 Matrix Product States
- 11 Infinite Matrix Product States
- 12 Determination of MPS
- 13 Continuous Matrix Product States
- 14 Classical Transfer Matrix Renormalization
- 15 Criterion of Truncation: Nonsymmetric Systems
- 16 Renormalization of Quantum Transfer Matrices
- 17 MPS Solution of QTMRG
- 18 Dynamical Correlation Functions
- 19 Time-Dependent Methods
- 20 Tangent-Space Approaches
- 21 Tree Tensor Network States
- 22 Two-Dimensional Tensor Network States
- 23 Coarse-Graining Tensor Renormalization
- Appendix Other Numerical Methods
- References
- Index
Summary
This chapter introduces the density matrix renormalization group (DMRG) in real space. The infinite and finite lattice algorithms of DMRG, and the approaches for targeting more than one eigenstate and for implementing DMRG in two dimensions by mapping a two-dimensional lattice onto a one-dimensional one, are discussed. The one-dimensional antiferromagnetic Heisenberg model of both integer and half-integer spins is used to demonstrate the method.
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- Density Matrix and Tensor Network Renormalization , pp. 103 - 122Publisher: Cambridge University PressPrint publication year: 2023