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
13 - Continuous Matrix Product States
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 constructs the MPS representation of a quantum state in the continuous limit. It starts with an MPS representation for the corresponding state in a discretized lattice system. Then the limit of the discretized lattice constant going to zero is taken to obtain its continuous presentation. The formulas for determining the expectation values are also derived. Finally, we discuss the scheme of canonicalization and the method for optimizing the local tensors of the continuous MPS.
- Type
- Chapter
- Information
- Density Matrix and Tensor Network Renormalization , pp. 204 - 216Publisher: Cambridge University PressPrint publication year: 2023