Bosonization and Strongly Correlated Systems

Detailed account of important technique for researchers and graduate students working in condensed matter and theoretical physics.

Alexander O. Gogolin (Author), Alexander A. Nersesyan (Author), Alexei M. Tsvelik (Author)

9780521617192, Cambridge University Press

Paperback, published 16 December 2004

448 pages, 90 b/w illus. 3 tables
24.6 x 18.9 x 2.3 cm, 0.8 kg

This 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.

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.

Subject Areas: Statistical physics [PHS]