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
17 - MPS Solution of QTMRG
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 reformulates QTMRG using the language of MPS and introduces the concept of bicanonical MPS and the method of biorthogonalization. The fixed-point equations for determining the local tensors of MPS in a translation-invariant system of one or more than one site in a unit cell are derived. The steps for solving these equations in the scheme of biorthonormalization are discussed.
- Type
- Chapter
- Information
- Density Matrix and Tensor Network Renormalization , pp. 258 - 272Publisher: Cambridge University PressPrint publication year: 2023