The Kondo Problem to Heavy Fermions

Front Cover
Cambridge University Press, Apr 28, 1997 - Science - 444 pages
This book deals with the concepts and techniques that have been developed to meet this challenge and with their application to the interpretation of experiment. The author surveys in detail the many-body techniques, scaling, renormalization group, Fermi liquid and Bethe ansatz, which lead to a solution of the Kondo problem for most of the theoretical models. The book also deals with special techniques for N-fold degenerate models for rare earth magnetic impurities. The many-body techniques developed to deal with strong correlation impurity problems have also been extended to provide a partial explanation of heavy fermion behavior.
 

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Contents

Models of Magnetic Impurities
1
12 Potential Scattering Model and the Friedel sum rule
4
13 Virtual Bound States
8
14 The NonInteracting Anderson Model
11
15 The sd Exchange Model
16
16 The Anderson Model U 0
17
17 Relation between the Anderson and sd Models
19
18 Parameter Regimes of the Anderson Model
21
Nfold Degenerate Models I
171
72 Perturbation Theory and the 1N Expansion
173
73 Exact Results
180
74 Fermi Liquid Theories
190
75 Slave Bosons and Mean Field Theory
196
NFold Degenerate Models II
205
82 The NonCrossing Approximation NCA
206
83 Beyond Mean Field Theory
213

19 The Ionic Model
23
110 The CoqblinSchrieffer Model
27
Resistivity Calculations and the Resistance Minimum
29
22 Conductivity and the Boltzmann Equation
32
23 Conductivity and Linear Response Theory
34
24 Kondos Explanation of the Resistance Minimum
38
The Kondo Problem
47
32 Beyond Perturbation Theory
50
33 Poor Mans Scaling
58
34 Scaling for the Anderson Model
65
Renormalization Group Calculations
71
42 Linear Chain Form for the sd Model
75
43 Logarithmic Discretization
78
44 The Numerical Renormalization Group Calculations
81
45 Effective Hamiltonians near the Fixed Points
85
46 High and Low Temperature Results
87
47 The Symmetric Anderson Model
93
48 The Asymmetric Anderson Model
98
Fermi Liquid Theories
103
52 The Generalized Friedel Sum Rule
110
53 Microscopic Fermi Liquid Theory
115
54 The Electrical Conductivity
121
55 Finite Order Perturbation Results
126
56 Renormalization Group Results for Spectral Densities
130
Exact Solutions and the Bethe Ansatz
135
62 Diagonalization of the sd Model
140
63 Excitations
146
64 Thermodynamics of the sd Model for S
151
65 Results for the sd Model S
156
66 Integrability of the Anderson Model
159
67 Results for the Symmetric Anderson Model
165
68 Results for the Asymmetric Anderson Model
168
84 The Variational 1N Expansion
223
Theory and Experiment
233
92 High Energy Spectroscopies
235
93 Thermodynamic Measurements
247
94 Transport Properties
273
95 Neutron Scattering
285
96 Local Measurements
291
97 The Possibility of First Principles Calculations?
309
Strongly Correlated Fermions
313
102 Anomalous Rare Earth Compounds
315
103 Heavy Fermions
323
104 Fermi Liquid Theory and Renormalized Bands
332
105 Mean Field Theory
338
106 Further Theoretical Approaches
347
107 The High Tc Superconductors
354
Scattering Theory
363
Linear Response Theory and Conductivity Formulae
367
The Zero Band Width Anderson Model
371
Scaling Equations for the CoqblinSchrieffer Model
375
Further Fermi Liquid Relations
381
The Algebraic Bethe Ansatz
387
The Wiener Hopf Solution
391
Rules for Diagrams
395
Perturbational Results to Order 1N
399
The nChannel Kondo Model for n 2S
403
Summary of Single Impurity Results
405
Reno finalized Perturbation Theory
411
Addendum
419
References
427
Index
439
Copyright

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Page 431 - In Handbook on the Physics and Chemistry of Rare Earths (eds KA Gschneidner, Jr and LR Eyring).
Page 427 - ABRIKOSOV, AA, GORKOV, LP, and DZYALOSHINSKI, IE, 1975, Methods of Quantum Field Theory in Statistical Physics (New York: Dover Publications).
Page 429 - Broholm, C., Kjems, JK, Aeppli, G., Fisk, Z., Smith, JL, Shapiro, SM, Shirane, GM Ott, HR (1987).
Page 428 - Bickers, NE (1987). Rev. Mod. Phys. 59, 845. Bickers, NE, Cox, DL & Wilkins, JH (1985).

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