Syllabus

The topics of this class will include

• • 1. Group theory and topology in Condensed Matter Physics. Application:

  • the Ten Fold Way classification of disordered topological insulators

  • and superconductors.

  • 2. Entanglement in many body systems. Relation to classical entropy.

  • Area laws and volume laws. Entanglement entropy in CFTs and

  • Topological entanglement entropy. Entanglement spectrum.

  • 3. Matrix Product States. Simple examples: AKLT state, Cat state. DMRG

  • algorithms, application for transverse field Ising model, spin chains

  • and the Haldane conjecture.

  • 4. Conformal Field Theory (CFT). Application to quantum Hall states

  • (bulk wave functions and edge states). Relation to statistical

  • mechanics models.

    • Bibliography

  • Jeffrey C. Y. Teo and C. L. Kane,

  • http://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.115120.

  • Shinsei Ryu, Andreas Schnyder, Akira Furusaki, Andreas Ludwig,

  • http://arxiv.org/abs/0912.2157.

  • U. Schollwock, Annals of Physics 326 (2011) 96–192.

  • P. Ginsparg, http://arxiv.org/abs/hep-th/9108028.