Bosonization and Strongly Correlated Systems

A. O. Gogolin, A. A. Nersesyan, Alexei M. Tsvelik

422 pages, parution le 16/12/2004

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Résumé

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.

Sommaire

Preface
Acknowledgements
Technical Aspects of Bosonization
- A simple case of Bose-Fermi equivalence: Jordan-Wigner transformation
- One-dimensional fermions. States near the Fermi points
- Gaussian model. Lagrangian formulation
- Conformal symmetry and finite size effects
- Virasoro algebra
- Structure of Hilbert space in conformal theories
- Current (Kac-Moody) algebras: the first assault
- Relevant and irrelevant fields
- Bose-Einstein condensation in two dimensions; Beresinskii-Kosterlitz-Thouless transition
- The sine-Gordon model
- Spin S=1/2 Heisenberg-Ising chain
- Ising model; 13. More about WZNW model
- Non-Abelian bosonization
Application of the Bosonization Technique to Physical Models in (1+1)-Dimensions
- Interacting fermions with spin
- Spin-1/2 Tomonaga-Luttinger liquid
- Instabilities of Tomonaga-Luttinger liquid
- Interacting fermions with broken spin rotational symmetry
- What happens with Tomonaga-Luttinger liquid in three dimensions
- Two weakly coupled Tomonaga-Luttinger liquids; spinless case
- Spin liquids in one dimension: example of spin-ladders
- Spin-1/2 Heisenberg chain with alternating exchange
- Superconductivity in a doped spin liquid
- Edge states in quantum Hall effect
Single Impurity Problems
- Potential scattering
- X-ray edge problem (Fermi liquids)
- Impurities in Tomonaga-Luttinger liquid
- Multi-channel Kondo problem
General Bibliography
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	A. O. Gogolin, A. A. Nersesyan, Alexei M. Tsvelik
Parution	16/12/2004
Nb. de pages	422
Format	19 x 24,5
Couverture	Broché
Poids	799g
Intérieur	Noir et Blanc
EAN13	9780521617192
ISBN13	978-0-521-61719-2