**[Cr:4, Lc:3, Tt:1, Lb:0]**

Knowledge of the content of **PHY302**, **PHY304** and **PHY402** is
essential to follow this course.

- Introduction and Motivation: Energy, length and time scales in solid state; complexity and emergent behavior; brief review of key concepts in quantum mechanics and statistical mechanics.
- Second quantization: Quantum fields as creation and annihilation operators; Fermi and Bose statistics; commutation and anticommutation relations.
- Tight-binding models and their applications: one-band and multi-band models; electronic structure and crystal lattices; metals and insulators; magnetic materials.
- Transition metal compounds: spin, charge and orbital degrees of freedom and their interplay; manganites; cuperates; pnictides.
- Phase Transitions: Examples of phase transitions; Ginzburg-Landau approach; Renormalization group methods.
- Special Topics (some of them will be as term papers): Strong coupling expansion; Monte-Carlo methods; Exact-diagonalization methods; BCS theory of superconductivity; double-exchange and Kondo-lattice models; Bose-Einstein condensation; Graphene and the quantum Hall effect.

- M. Tinkham, Introduction to Superconductivity, Dover Publications (2004).
- C. J. Pethick and H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press (2008).
- G. D. Mahan, Many Particle Physics, Springer (2010).
- N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Westview Press (1992).
- A. L. Fetter and J. D. Walecka, Quantum Theory of Many Particle Systems, Dover Publications (2003).
- P. Fazekas, Lecture Notes on Electron Correlation and Magnetism, World Scientific (1999).
- N. W. Ashcroft and N. D. Mermin, Solid State Physics, Brooks Cole (1976).