Book contents
- Frontmatter
- Contents
- Preface
- Preface to paperback edition
- Brief History
- 1 Models of Magnetic Impurities
- 2 Resistivity Calculations and the Resistance Minimum
- 3 The Kondo Problem
- 4 Renormalization Group Calculations
- 5 Fermi Liquid Theories
- 6 Exact Solutions and the Bethe Ansatz
- 7 N-fold Degenerate Models I
- 8 N-fold Degenerate Models II
- 9 Theory and Experiment
- 10 Strongly Correlated Fermions
- Appendix A Scattering Theory
- Appendix B Linear Response Theory and Conductivity Formulae
- Appendix C The Zero Band Width Anderson Model
- Appendix D Scaling Equations for the Coqblin–Schrieffer Model
- Appendix E Further Fermi Liquid Relations
- Appendix F The Algebraic Bethe Ansatz
- Appendix G The Wiener–Hopf Solution
- Appendix H Rules for Diagrams
- Appendix I Perturbational Results to Order 1/N
- Appendix J The n-Channel Kondo Model for n > 2S
- Appendix K Summary of Single Impurity Results
- Appendix L Renormalized Perturbation Theory
- Addendum
- References
- Index
10 - Strongly Correlated Fermions
Published online by Cambridge University Press: 22 September 2009
- Frontmatter
- Contents
- Preface
- Preface to paperback edition
- Brief History
- 1 Models of Magnetic Impurities
- 2 Resistivity Calculations and the Resistance Minimum
- 3 The Kondo Problem
- 4 Renormalization Group Calculations
- 5 Fermi Liquid Theories
- 6 Exact Solutions and the Bethe Ansatz
- 7 N-fold Degenerate Models I
- 8 N-fold Degenerate Models II
- 9 Theory and Experiment
- 10 Strongly Correlated Fermions
- Appendix A Scattering Theory
- Appendix B Linear Response Theory and Conductivity Formulae
- Appendix C The Zero Band Width Anderson Model
- Appendix D Scaling Equations for the Coqblin–Schrieffer Model
- Appendix E Further Fermi Liquid Relations
- Appendix F The Algebraic Bethe Ansatz
- Appendix G The Wiener–Hopf Solution
- Appendix H Rules for Diagrams
- Appendix I Perturbational Results to Order 1/N
- Appendix J The n-Channel Kondo Model for n > 2S
- Appendix K Summary of Single Impurity Results
- Appendix L Renormalized Perturbation Theory
- Addendum
- References
- Index
Summary
Introduction
Our main concern so far has been with theories of a single magnetic impurity in a simple host metal. These theories have been developed over a period of more than thirty years and most of the models put forward for explaining these systems are now well understood. The concepts for understanding their behaviour in terms of scaling trajectories, fixed points, spin compensation, quasi-particles, Fermi liquid theory and Kondo resonances have been developed and there are exact solutions for the thermodynamic behaviour of many of the models as well as good approximations for their dynamic response (for the reader who has skipped the details of chapters 4–8 the important single impurity results are summarized in appendix K). As we saw in the previous chapter there is still much to be done in the way of detailed predictions for specific systems to compare with experiment. There is also the possibility of new types of experiments to probe the theory further (for example, the possibility of probing the Kondo resonance by resonant tunnelling has recently been discussed by Hershfield, Davies and Wilkins, 1991). These may throw up new puzzles to be answered. The general belief, however, is that if these occur they will be relatively minor and will not require a fundamental reworking of the theory. With these provisos it may be claimed the single impurity problem has been ‘solved’.
- Type
- Chapter
- Information
- The Kondo Problem to Heavy Fermions , pp. 313 - 362Publisher: Cambridge University PressPrint publication year: 1993