Preface ......................................................... xi
1 Introduction .................................................. 1
1.1 Spontaneously broken symmetry ............................ 1
1.2 Tracking broken symmetry: order parameter ................ 4
1.3 Beyond broken symmetry ................................... 7
References .................................................... 9
2 Non-interacting electron gas ................................. 10
Problems ..................................................... 15
3 Born-Oppenheimer approximation ............................... 16
3.1 Basic Hamiltonian ....................................... 16
3.2 Adiabatic approximation ................................. 17
3.3 Tight-binding approximation ............................. 20
Problem ...................................................... 22
References ................................................... 23
4 Second quantization .......................................... 24
4.1 Bosons .................................................. 24
4.2 Fermions ................................................ 26
4.3 Fermion operators ....................................... 27
Problems ..................................................... 30
References ................................................... 30
5 Hartree-Fock approximation ................................... 31
5.1 Non-interacting limit ................................... 31
5.2 Hartree-Fock approximation .............................. 33
5.3 Diagrams ................................................ 35
Problem ...................................................... 36
References ................................................... 36
6 Interacting electron gas ..................................... 37
6.1 Uniform electron gas .................................... 38
6.2 Hartree-Fock excitation spectrum ........................ 40
6.3 Cohesive energy of metals .............................. 42
Summary ...................................................... 48
Problems ..................................................... 48
References ................................................... 49
7 Local magnetic moments in metals ............................. 51
7.1 Local moments: phenomenology ............................ 51
7.2 Impurity density of states .............................. 54
7.3 Green functions ......................................... 60
7.4 Friedel's sum rule and local moments .................... 70
Summary ...................................................... 74
Appendix to Chapter 7: Luttinger's theorem ................... 74
Problems ..................................................... 79
References ................................................... 79
8 Quenching of local moments: the Kondo problem ................ 80
8.1 The Kondo Hamiltonian ................................... 82
8.2 Why is J negative? ...................................... 83
8.3 Scattering and the resistivity minimum .................. 87
8.4 Electron-impurity scattering amplitudes ................. 94
8.5 Kondo temperature ....................................... 99
8.6 Poor Man's scaling ..................................... 102
Summary ..................................................... 109
Appendix to Chapter 8: the Schrieffer-Wolff transformation .. 109
Problems .................................................... 113
References .................................................. 114
9 Screening and plasmons ...................................... 115
9.1 Thomas-Fermi screening ................................. 115
9.2 Plasma oscillations and collective coordinates ......... 117
9.3 Linear response theory ................................. 122
9.4 Dielectric response function ........................... 127
9.5 Kubo formula: electrical conductivity .................. 137
9.6 Stopping power of a plasma ............................. 140
Summary ..................................................... 143
Problems .................................................... 144
References .................................................. 145
10 Bosonization ................................................ 146
10.1 Luttinger liquid ....................................... 146
10.2 Bosonization of Luttinger model ........................ 151
10.3 Pair binding: can electrons do it alone? ............... 160
10.4 Excitation spectrum .................................... 162
Summary ..................................................... 167
Problems .................................................... 167
References .................................................. 168
11 Electron-lattice interactions ............................... 169
11.1 Harmonic chain ......................................... 169
11.2 Acoustic phonons ....................................... 171
11.3 Electron-phonon interaction ............................ 172
11.4 Ultrasonic attenuation ................................. 176
11.5 Electrical conduction .................................. 178
Summary ..................................................... 187
Problems .................................................... 187
References .................................................. 188
12 Superconductivity in metals ................................. 189
12.1 Superconductivity: phenomenology ....................... 189
12.2 Electron-phonon effective interaction .................. 197
12.3 Model interaction ...................................... 199
12.4 Cooper pairs ........................................... 201
12.5 Fermi liquid theory .................................... 205
12.6 Pair amplitude ......................................... 216
12.7 BCS ground state ....................................... 221
12.8 Pair fluctuations ...................................... 224
12.9 Ground state energy .................................... 226
12.10 Critical magnetic field ............................... 229
12.11 Energy gap ............................................ 231
12.12 Quasi-particle excitations ............................ 233
12.13 Thermodynamics ........................................ 237
12.14 Experimental applications ............................. 241
12.15 Josephson tunneling ................................... 253
Summary ..................................................... 255
Problems .................................................... 255
References .................................................. 257
13 Disorder: localization and exceptions ....................... 258
13.1 Primer on localization ................................. 259
13.2 Return probability: localization criterion ............. 261
13.3 Weak localization ...................................... 264
13.4 Scaling theory ......................................... 269
13.5 Exceptions to localization ............................. 275
Summary ..................................................... 285
Problems .................................................... 286
References .................................................. 287
14 Quantum phase transitions ................................... 289
14.1 Quantum rotor model .................................... 291
14.2 Scaling ................................................ 293
14.3 Mean-field solution .................................... 296
14.4 Landau-Ginsburg theory ................................. 302
14.5 Transport properties ................................... 306
14.6 Experiments ............................................ 308
14.7 Scaling and T-linear resistivity ....................... 310
Problems .................................................... 314
References .................................................. 314
15 Quantum Hall and other topological states ................... 317
15.1 What is the quantum Hall effect? ....................... 317
15.2 Landau levels .......................................... 320
15.3 The role of disorder ................................... 324
15.4 Currents at the edge ................................... 326
15.5 Topological insulators ................................. 330
15.6 Laughlin liquid ........................................ 343
Summary ..................................................... 349
Problems .................................................... 349
References .................................................. 350
16 Electrons at strong coupling: Mottness ...................... 353
16.1 Band insulator ......................................... 354
16.2 Mott's problem ......................................... 357
16.3 Much ado about zeros: Luttinger surface ................ 363
16.4 Beyond the atomic limit: Heisenberg versus Slater ...... 368
16.5 Dynamical spectral weight transfer ..................... 380
16.6 Epilogue: 1 = 2 - 1 .................................... 396
Problems .................................................... 397
References .................................................. 398
Index .......................................................... 400
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