Topology in condensed matter physics
Lecture in summer term 2023.
Lecturer: Thore Posske
Course assistent: Ioannis Ioannidis
Script
Script of current course
Organization
Schedule:
Lecture: Wed, 10:00 a.m. - 11:30 a.m., Jungiusstr. 11, A208
Exercises: Wed, 11:45 a.m. - 1:15 p.m., Jungiusstr. 11, blue saloon, B120
Only online lecture on: May 10, Conference
No lecture: May 17, Pentecost vacations
Last lecture: Wed, July 12.
Special lectures: June 28 and July 5: Guest lecture by Benedetta Flebus (Boston College, Mildred Dresselhaus guest professor), Nonhermitian physics and the Su-Schrieffer-Heeger model
Topics, recommendations, and literature
Consent for video recording
Zoom-link
Exam
Exam/orals on Wed, August 2, 10 a.m. - 2 p.m..
Voted on in second lecture
Oral, 30 minutes. Take care of the concrete appointments by writing me an email.
There will be a Questions and Answers session the Friday before the exam starting at 10:00 a.m..
Please send questions in advance.
Content
Video streaming page
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Questions and answers session (July 28)
Questions and answers
Video 13
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Script 13 |
Exercise Sheet 13 |
Solutions 13
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Special Lecture (July 5)
The nonhermitian SSH model (Benedetta Flebus)
Video 1
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Video 2
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Script SSH
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Preperatory Exercise Sheet SSH
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Challenge
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Lecture 11 (June 21)
Configuration spaces and anyons
Video 11
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Script 11
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Exercise Sheet 11
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Solutions 11
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Lecture 10 (June 14)
Proof of the adiabatic theorem of quantum mechanics
Video 10
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Script 10
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Exercise Sheet 10
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Solutions 10
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Lecture 9 (June 6)
Topological quantum computing and the adiabatic theorem of quantum mechanics
Video 9
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Script 9
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Exercise Sheet 9
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Solutions 9
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Lecture 8 (May 31)
The Kitaev Majorana chain
Video 8
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Script 8
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Exercise Sheet 8
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Solutions 8
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Lecture 7 (May 25)
Classification of topological phases, final comments and the Su-Schrieffer-Heeger model
Video 7
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Script 7
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Exercise Sheet 7
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Solutions 7
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Lecture 6 (May 16)
The tenfold way (periodic table of topological matter)
Video 6.1 (hint for current exercise sheet)
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Video 6.2 (Diagonalizing translational invariant noninteracting models)
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Video 6.3 (Example classification in case of no symmetry)
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Video 6.4 (Action of symmetry on the target space)
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Video 6.5 (The tenfold way table)
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Script 6
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Exercise Sheet 6 |
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Lecture 5 (May 3)
Classification of topological phases, (anti)unitary symmetries T, P, C
Video 5
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Script 5 |
Exercise Sheet 5
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Solutions 5
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Lecture 4 (April 26)
The first homotopy group (fundamental group), Classification of electronic topological matter.
ONLY AUDIO RECORDING OF THE LECTURE.
Video 4
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Script 4 |
Exercise Sheet 4
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Solutions 4
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Lecture 3 (April 19)
Quotient space, fiber bundle, topological invariants, paths, homotopy
Video 3
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Script 3 |
Exercise Sheet 3
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Solutions 3
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Lecture 2 (April 12)
Continuous functions, homeomorphisms, construction of topological spaces
Video 2
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Script 2
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Exercise Sheet 2
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Solutions 2
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Lecture 1 (April 5)
Administration and inspiration
Video 1
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Script 1
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Exercise Sheet 1
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Solutions 1
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All lectures
Script of current course
Script of previous course
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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 In Condensed Matter: An Introduction - Miguel A N Araujo and Pedro Sacramento
Quantum Computation and Quantum Information - Michael Nielsen and Isaac Chuang
Altland's and Simons' book on Condensed Matter theory
Course on topology in condensed matter physics by Akhmerov et al.
Topology and physics - a historical essay, C. Nash
Topological Quantum Computation-From 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, non-interacting, topological phases
Ryu, Schnyder, Furusaki, Ludwig, classification of gapped, non-interacting, topological phases
Katos seminal paper about adiabatic time evolution
