8.513  Condensed Matter Physics: Symmetry, Topology and Coherence in Many-Particle Systems

The aim of the course is to two-fold. Our first goal will be to discuss the concepts of condensed matter theory such as symmetry, topology and their relation to different types of ordering in many-particle systems. Our second goal will be to provide a gentle introduction to methods of quantized fields and their applications in many-body physics. We shall try to emphasize the physical and visualizable aspects of the subject. While the course is intended for students with a wide range of interests, many examples will be drawn from condensed matter physics and atomic physics.

Course topics (tentative):

• Second quantization; path integrals in quantum mechanics

• Symmetries and broken symmetries. Conservation laws, hydrodynamics
• Symmetries and phase transitions. Goldstone theorem
• Topology of Bloch bands. Chern number and quantization of observables.
• Different types of symmetry breaking (SB). Spontaneous SB and phase transitions. Superfluidity and magnetism.
• Anomalous SB. Chiral anomaly and scaling anomaly in condensed matter systems.
• Free fermion systems. Interacting fermion systems. Landau Fermi liquid theory.
• Interacting one-dimensional systems. Luttinger liquids. Fractionalization of quantum numbers.
• Theory of quantum Hall effects. Aharonov-Bohm effect and fractional statistics.

 

Problem sets weekly, 12 total, due Thursday in class

Term paper (presentations on the last day of classes)

Grade: Psets 70% Term paper 30%