Bosonization and Strongly Correlated Systems
Bosonization and Strongly Correlated Systems
Alexander A. Nersesyan, Tbilisi Institute of Physics, Georgia
Alexei M. Tsvelik, University of Oxford
£50.99
GBPThis volume provides a detailed account of bosonization. This important technique represents one of the most powerful nonperturbative approaches to many-body systems currently available. The first part of the book examines the technical aspects of bosonization. Topics include one-dimensional fermions, the Gaussian model, the structure of Hilbert space in conformal theories, Bose-Einstein condensation in two dimensions, non-Abelian bosonization, and the Ising and WZNW models. The second part presents applications of the bosonization technique to realistic models including the Tomonaga-Luttinger liquid, spin liquids in one dimension and the spin-1/2 Heisenberg chain with alternating exchange. The third part addresses the problems of quantum impurities. Chapters cover potential scattering, the X-ray edge problem, impurities in Tomonaga-Luttinger liquids and the multi-channel Kondo problem. This book will be an excellent reference for researchers and graduate students working in theoretical physics, condensed matter physics and field theory.
- Topic of considerable interest
- Leading authors
- Contains interesting sketches of leading figures in the field, many exercises included
Product details
December 2004Paperback
9780521617192
448 pages
246 × 189 × 23 mm
0.8kg
90 b/w illus. 3 tables
Available
Table of Contents
- Preface
- Acknowledgements
- Part I. Technical Aspects of Bosonization:
- 1. A simple case of Bose-Fermi equivalence: Jordan-Wigner transformation
- 2. One-dimensional fermions. States near the Fermi points
- 3. Gaussian model. Lagrangian formulation
- 4. Conformal symmetry and finite size effects
- 5. Virasoro algebra
- 6. Structure of Hilbert space in conformal theories
- 7. Current (Kac-Moody) algebras: the first assault
- 8. Relevant and irrelevant fields
- 9. Bose-Einstein condensation in two dimensions
- Beresinskii-Kosterlitz-Thouless transition
- 10. The sine-Gordon model
- 11. Spin S=1/2 Heisenberg-Ising chain
- 12. Ising model
- 13. More about WZNW model
- 14. Non-Abelian bosonization
- Part II. Application of the Bosonization Technique to Physical Models in (1+1)-Dimensions:
- 15. Interacting fermions with spin
- 16. Spin-1/2 Tomonaga-Luttinger liquid
- 17. Instabilities of Tomonaga-Luttinger liquid
- 18. Interacting fermions with broken spin rotational symmetry
- 19. What happens with Tomonaga-Luttinger liquid in three dimensions
- 20. Two weakly coupled Tomonaga-Luttinger liquids
- spinless case
- 21. Spin liquids in one dimension: example of spin-ladders
- 22. Spin-1/2 Heisenberg chain with alternating exchange
- 23. Superconductivity in a doped spin liquid
- 24. Edge states in quantum Hall effect
- Part III. Single Impurity Problems:
- 25. Potential scattering
- 26. X-ray edge problem (Fermi liquids)
- 27. Impurities in Tomonaga-Luttinger liquid
- 28. Multi-channel Kondo problem
- General Bibliography
- Index.
