


Condensed Matter Theory, PHAS0059
 Course Outline and Lecture Notes
1. From the Harmonic Oscillator to Phonons 
 The Harmonic Oscillator
 Two Coupled Oscillators
 The Harmonic Chain
 Specific Heat of Phonons in the Harmonic Crystal

2. Second Quantisation

 Identical Particles
 Occupation Numbers and Fock Space
 Creation and Annihilation Operators
 Transformation between Bases
 Single and TwoParticle Operators
 Unitary and Bogoliubov Transformations

3. The WeaklyInteracting Bose Gas 
 BoseEinstein Condensation
 Mean Field Theory of Weakly Interacting Bose Gas
 Landau's Critical Superfluid Velocity
 Superfluid Fraction

4. Quantum Magnets 
 The Heisenberg Model
 HolsteinPrimakoff Transformation
 Linear SpinWave Theory
 The Heisenberg Ferromagnet
 The Heisenberg Antiferromagnet
 OneDimensional Spin Chains
 Haldane's Conjecture
 JordanWigner Transformation for S=1/2 chains
 The Haldane S=1 chain, AKLT Model

5. The Free Fermi Gas 
 Fermi Function and Density of States
 The Sommerfeld Expansion

6. Landau Theory of Fermi Liquids 
 Lifetime of Quasiparticles
 Relation between bare Fermions and Quasiparticles
 Parametrising Excitation Energies
 Measuring the Landau Parameters

7. BCS Theory of Superconductivity 
 ElectronPhonon Interaction
 The Cooper Problem
 The Role of the Coulomb Repulsion
 The BCS Wave Function
 BCS Mean Field Theory

8. Strong Correlations 
 TightBinding Approximation
 The Hubbard Model
 Mott Insulators and Antiferromagnetism
 The Mott Transition
 Magnetic Impurities in Metals
 The Anderson Impurity Model
 The Kondo Model
 The Kondo Problem

9. Topology in Condensed Matter 
 Topological Invariants
 Integer Quantum Hall Effect and Chern Numbers
 The Haldane Model
 BulkBoundary Correspondence

 Main Suggested Texts
 See the lecture notes of Prof John Chalker with which this course has a large overlap
http://wwwthphys.physics.ox.ac.uk/people/JohnChalker/qtcm/lecturenotes.pdf
 N.W. Ashcroft and N.D. Mermin, Solid State Physics, HoltSanders (1976).
 A. Auerbach, Interacting Electrons and Quantum Magnetism, Springer (1994).
A good introduction to a range of current theoretical ideas.
 S.K. Ma, Statistical Mechanics, World Scientific (1985).
Strongly recommended book at a level suitable for first year graduate students.
 J.P. Blaizot and G. Ripka, Quantum Theory of Finite Systems, MIT (1986).
A very thorough treatment of second quantisation, canonical transformations and
selfconsistent field approximations.
 P.W. Anderson, Concepts in Solids, Benjamin (1963).
A classic introduction to solid state physics at a graduate level.
 D. Pines and P. Nozieres, The Theory of Quantum Liquid, Addison Wesley (1989).
A standard account of Fermi liquids.
 P.W. Anderson, Basic Notions in Condensed Matter Physics, Benjamin (1984).
An advanced discussion of some of the most important ideas in the subject.
 More Advanced Graduate Text
 A. Altland and B.D. Simons Quantum Field Theory in Condensed Matter Physics,
Cambridge University Press (2006).
An accessible introduction to the subject.



