An introduction to topological matter – from gauge theories to insulators

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Syllabus [pdf file]

First part: gauge theories and spin liquids

First two lectures – Feb. 27 [2pm] and 28 [9am]

  • Brief intro on lattice gauge theories
  • Confinement and deconfinement in Ising-gauge theories: non-local order parameters and toplogical quantum spin liquids
  • Dual description of Ising gauge theories
  • Quantum dimer models and U(1) spin liquids

3rd lecture – Mar. 7 [9am]

  • Entanglement and topology: entanglement entropy and entanglement spectra
  • Braiding statisics, anyons. Examples with the toric code

Second part: non-local order in one-dimensional spin liquids

4th-5th lecture – Mar. 8 and 9 [9am]

  • One-dimensional ‘spin-liquids’ – hidden order
  • The Haldane chain: string order, hidden symmetries, Kennedy-Tasaki transformation
  • Edge states
  • Spin-1/2 chains with hidden order

Third part: non-interacting topological matter

6th lecture – Mar. 14 [9am]

  • Kitaev model: phase diagram, solution
  • Majorana edge modes

7th lecture – Mar. 21 [9am]

  • Integer quantum Hall effect: experimental facts and particles in a magnetic field
  • Current quantization and theoretical interpretation

8th lecture – Mar. 23 [9am]

  • Towards the Altland-Zirnbauer classification of non-interacting topological matter

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