Density Matrix and Tensor Network Renormalization

This book provides a comprehensive introduction to the theory of tensor network renormalization for the first time. An accessible primer for scientists and engineers, this book would also be ideal as a reference text for a graduate course in this area.

List of contents

Preface; Abbreviations; Unit used; Notations and graphical representations; 1. Introduction; 2. Basic algebra of tensors; 3. Tensor network representation of classical statistical methods; 4. Tensor-network ansatz of wave functions; 5. Criterion of truncation: symmetric systems; 6. Real-space DMRG; 7. Implementation of symmetries; 8. DMRG with non-local basis states; 9. Matrix Product States; 10. Infinite Matrix Product States; 11. Determination of MPS; 12. Continuous Matrix Product States; 13. Classical Transfer Matrix Renormalization; 14. Criterion of truncation: non-symmetric systems; 15. Renormalization of quantum transfer matrices; 16. MPS solution of QTMRG; 17. Dynamical Correlation Functions; 18. Time-dependent methods; 19. Tangent-space operations; 20. Tangent-space approaches; 21. Tree Tensor Network States; 22. Two-dimensional tensor network states; 23. Coarse graining tensor renormalization; Appendix A; References; Index.

About the author

Tao Xiang is Professor at the Institute of Physics, Chinese Academy of Sciences (CAS), and specializes in condensed matter theory. He is a CAS academician and a fellow of the World Academy of Sciences, and has received the He-Leung-He-Lee Prize for Scientific and Technological Progress, among other awards.

Product details

• Authors: Tao Xiang, Tao (Chinese Academy of Sciences Xiang, Xiang Tao
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.08.2023
• EAN: 9781009398701
• ISBN: 978-1-0-0939870-1
• No. of pages: 470
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Mechanics, acoustics; machine learning, SCIENCE / Physics / General, SCIENCE / Physics / Condensed Matter, computer science, Statistical physics, Designed for home learning, COMPUTERS / Data Science / Machine Learning, For graduate / post-graduate and equivalents, Quantum computing and information, For home learning: advanced levels, COMPUTERS / Quantum Computing