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
Appendix H - Rules for Diagrams
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
Rules for Diagrams
Here we summarize the rules for drawing and evaluating the diagrams for the perturbational contributions to the resolvent Rα(z), defined in equation (7.8), for the degenerate Anderson model. The expansion is in powers of the hybridization parameter V. We give rules for the U = ∞ model and general N.
(1) Each diagram has a base line running from left to right which corresponds to the impurity state. A full line with an arrow directed from left to right and a label m indicates an occupied state f, nf = 1, m. A dashed line represents the unoccupied state nf = 0. The initialand final lines correspond to the state |α〉.
(2) The vertices are associated with the interaction (7.10), at which a single conduction electron (full line) is created or annihilated. When the arrow is directed away from the vertex the electron is created, when directed towards the vertex it is annihilated. Contributions of the order |V|2n correspond to all possible diagrams with 2n vertices consistent with the direction of the arrows.
(3) Quantum numbers k, m, are assigned to each conduction line and have an associated factor, for lines running from left to right, and a factor, for lines running in the reverse direction. The z-component of angular momentum, m, is conserved at each vertex.
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- The Kondo Problem to Heavy Fermions , pp. 395 - 398Publisher: Cambridge University PressPrint publication year: 1993