1 Introduction

1.1 Spontaneously broken symmetry

1.2 Tracking broken symmetry:order parameter

1.3 Beyond broken symmetry

References

2 Non-interacting electron gas

Problems

3 Born-Oppenheimer approximation

3.1 Basic Hamiltonian

3.2 Adiabatic approximation

3.3 Tight-binding approximation

Problem

References

4 Second quantization

4.1 Bosons

4.2 Fermions

4.3 Fermion operators

Problems

References

5 Hartree-Fock approximation

5.1 Non-interacting limit

5.2 Hartree-Fock approximation

5.3 Diagrams

Problem

References

6 Interacting electron gas

6.1 Uniform electron gas

6.2 Hartree-Fock excitation spectrum

6.3 Cohesive energy of metals

Summary

Problems

References

7 Local magnetic moments in metals

7.1 Local moments:phenomenology

7.2 Impurity density of states

7.3 Green functions

7.4 Friedel's sum rule and local moments

Summary

Appendix to Chapter 7:Luttinger's theorem

Problems

References

8 Quenching of local moments:the Kondo problem

8.1 The Kondo Hamiltonian

8.2 Why is J negative?

8.3 Scattering and the resistivity minimum

8.4 Electron-impurity scattering amplitudes

8.5 Kondo temperature

8.6 Poor Man's scaling

Summary

Appendix to Chapter 8:the Schrieffer-Wolff transformation

Problems

References

9 Screening and plasmons

9.1 Thomas-Fermi screening

9.2 Plasma oscillations and collective coordinates

9.3 Linear response theory

9.4 Dielectric response function

9.5 Kubo formula:electrical conductivity

9.6 Stopping power of a plasma

Summary

Problems

References

10 Bosonization

10.1 Luttinger liquid

10.2 Bosonization of Luttinger model

10.3 Pair binding:can electrons do it alone?

10.4 Excitation spectrum

Summary

Problems

References

11 Electron-Iattice interactions

11.1 Harmonic chain

11.2 Acoustic phonons

11.3 Electron-phonon interaction

11.4 Ultrasonic attenuation

11.5 Electrical conduction

Summary

Problems

References

12 Superconductivity in metals

12.1 Superconductivity:phenomenology

12.2 Electron-phonon effective interaction

12.3 Model interaction

12.4 Cooper pairs

12.5 Fermi liquid theory

12.6 Pair amplitude

12.7 BCS ground state

12.8 Pair fluctuations

12.9 Ground state energy

12.10 Critical magnetic field

12.11 Energy gap

12.12 Quasi-particle excitations

12.13 Thermodynamics

12.14 Experimental applications

12.15 Josephson tunneling

Summary

Problems

References

13 Disorder:localization and exceptions

13.1 Primer on localization

13.2 Return probability:localization criterion

13.3 Weak localization

13.4 Scaling theory

13.5 Exceptions to localization

Summary

Problems

References

14 Quantum phase transitions

14.1 Quantum rotor model

14.2 Scaling

14.3 Mean-field solution

14.4 Landau-Ginsburg theory

14.5 Transport properties

14.6 Experiments

14.7 Scaling and T-linear resistivity

Problems

References

15 Quantum Hall and other topological states

15.1 What is the quantum Hall effect?

15.2 Landau levels

15.3 The role of disorder

15.4 Currents at the edge

15.5 Topological insulators

15.6 Laughlin liquid

Summary

Problems

References

16 Electrons at strong coupling:Mottness

16.1 Band insulator

16.2 Mott's problem

16.3 Much ado about zeros:Luttinger surface

16.4 Beyond the atomic limit:Heisenberg versus Slater

16.5 Dynamical spectral weight transfer

16.6 Epilogue:1＝2-1

Problems

References

Index