Exact Methods in Low-dimensional Statistical Physics and Quantum Computing : Lecture Notes of the Les Houches Summer School: Volume 89, July 2008 (Lecture Notes of the Les Houches Summer School)

Jacobsen, Jesper (EDT)/ Ouvry, Stephane (EDT)/ Pasquier, Vincent (EDT)

Oxford University Press（2010/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 652 p.
• 言語 ENG
• 商品コード 9780199574612
• DDC分類 530.133

Full Description

Recent years have shown important and spectacular convergences between techniques traditionally used in theoretical physics and methods emerging from modern mathematics (combinatorics, probability theory, topology, algebraic geometry, etc). These techniques, and in particular those of low-dimensional statistical models, are instrumental in improving our understanding of emerging fields, such as quantum computing and cryptography, complex systems, and quantum fluids. This book sets these issues into a larger and more coherent theoretical context than is currently available. For instance, understanding the key concepts of quantum entanglement (a measure of information density) necessitates a thorough knowledge of quantum and topological field theory, and integrable models. To achieve this goal, the lectures were given by international leaders in the fields of exactly solvable models in low dimensional condensed matter and statistical physics.

Contents

LECTURES ; 1. Quantum impurity problems in condensed matter physics ; 2. Conformal field theory and statistical mechanics ; 3. Quantum Hall effect ; 4. Topological quantum phases and quantum computation ; 5. Four lectures on computational statistical physics ; 6. Loop models ; 7. Lectures on the integrability of the 6-vertex model ; 8. Mathematical aspects of 2D phase transitions ; 9. Numerical simulations of quantum statistical mechanics models ; 10. Rapidly rotating atomic Bose gases ; 11. Quantum Hall effect ; 12. The dimer model ; 13. Boundary loop models and 2D quantum gravity ; 14. Real-space condensation in stochastic mass transport models ; 15. Quantum spin liquids ; 16. Super spin chains and super sigma models: a short introduction ; 17. Integrability and combinatorics: selected topics ; SEMINARS ; 18. A rigorous perspective on Liouville quantum gravity and KPZ ; 19. Topologically protected qubits based on Josepshon junction arrays ; 20. On some quantum Hall states with negative flux ; 21. Supersolidity and what soluble models can tell us about it