PH-605 Condensed Matter Theory-I

1. Introduction: Overview of modern condensed matter physics, more is different, emergent properties.
2. Broken symmetry, quasiparticles and collective phenomena: Symmetry, importance of broken symmetry, adiabatic continuity and universality.
3. Landau’s Fermi liquid theory: The free electron theory, why does the free electron theory work so well? Adiabatic continuity applied to Fermi systems, Landau’s Fermi liquid theory, physical consequences.
4. Second quantization and its applications: Bosons, Fermions, Fermion operators, quantum magnetism, spin waves and magnons, Su-Shriefer-Heeger model of a conducting polymer chain.
5. Electron interactions: Hartree and Hartree-Fock theory, Metals in the Hartree-Fock approximation, correlation energy of jellium, Wigner crystallization, Inhomogeneous electron systems, Kohn-Hohenberg theory, The Kohn-Sham equation, Exchange-correlation functional.
6. Response functions: An overview of modern experimental techniques, linear response theory, fluctuation-dissipation theorem, dielectric response function.
7. Luttinger liquid theory: Why is 1D special? The Luttinger model, spin-charge separation.
8. Electron-lattice interactions: harmonic chain, electron-phonon interaction, electrical conduction, effective electron-electron coupling.

Recommended texts:

• Advanced Solid State Physics, by P. Philips, publisher: Westview Press; 1st edition, (2003).
• Condensed Matter Field Theory, by A. Altland and B. Simons, publisher: Cambridge University Press, 1st edition (2006).
• Advanced Condensed Matter Physics, by L. M. Sander, publisher: Cambridge University Press, 1st edition (2009).