Topology in condensed matter physics
Organization
Lecture in summer term 2016.
Schedule: Tue, 10:15  11:45 lecture, 12:25  13:55 exercise group
No lectures: May 5 2016: Christi Himmelfahrt (Ascension), May 19 2016: Pfingstferien (Pentecost)
Topics, recommandations, and literature
Exam
Exam: oral, 30 minutes. Please take care of the concrete appointments by yourselves by writing me an email.
Possible dates:
30.8. afternoon
31.8. afternoon
1.9. morning
There will be a Questions and Answers session on August 25 starting at 13:00 in seminar room 1.
Please send questions in advance.
Content
Video streaming page

Lecture 12 (July 14)
Proof of the adiabatic theorem and its geometric interpretation
Video 12

Script 12

Exercise Sheet 13 
Solutions 13

Lecture 11 (July 7)
Topological quantum computing and the adiabatic theorem of quantum mechanics
Video 11

Script 11

Exercise Sheet 12 
Solutions 12

Lecture 10 (June 30)
The Kitaev Majorana chain II and quantum computing
Video 10

Script 10

Exercise Sheet 11

Solutions 11

Lecture 9 (June 23)
The Kitaev Majorana chain I
Video 9

Script 9

Exercise Sheet 10

Solutions 10

Lecture 8 (June 16)
The tenfold way
Video 8

Script 8

Exercise Sheet 9

Solutions 9

Lecture 7 (June 9)
classification of topological phases, (anti)unitary symmetries T, P, C
Video 7

Script 7

Exercise Sheet 8

Solutions 8

Lecture 6 (June 2)
particle on a ring, definition of topological gapped phase
Video 6

Script 6

Exercise Sheet 7

Solutions 7

Lecture 5 (May 12)
configuration spaces, path integral quantization, and anyons
Video 5

Script 5

Exercise Sheet 6

Solutions 6

Lecture 4 (April 28)
the first homotopy group (fundamental group), indiscernible particles
Video 4

Script 4

Exercise Sheet 5

Solutions 5

Lecture 3 (April 21)
quotient space, fiber bundle, topological invariants, paths, homotopy
Video 3

Script 3

Exercise Sheet 4

Solutions 4

Lecture 2 (April 14)
continuous functions, homeomorphisms, construction of topological spaces
Video 2

Script 2

Exercise Sheet 3

Solutions 3

Lecture 1 (April 7)
organization, content, motivation, and first definitions
Video 1 
Script 1 
Exercises 1, 2 
Solutions 1, 2
toggler:
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Additional material
Video lecture by John Milnor (Fields medalist, "Milnor spheres") about differential topology
Video lectures by Norman Wildberger about algebraic topology explained very intuitively
Video that the torus can be folded to a Moebius strip and corresponding Mathematica notebook
Notebook for numerically experimenting with the Kitaev chain's spectrum and topological phases
Recommended reading/references
Topology and physics  a historical essay, C. Nash
Topological Quantum ComputationFrom Basic Concepts to First Experiments, Stern, Ady and Lindner, Netanel H.
Seminal paper of Leinaas and Myrheim '77 describing anyons
Philosophical background on the "principle of indiscernibles"
Kitaev's periodic table of gapped, noninteracting, topological phases
Ryu, Schnyder, Furusaki, Ludwig, classification of gapped, noninteracting, topological phases
Katos seminal paper about adiabatic time evolution