⚠️ Anstehende Plugin-Deinstallation | Upcoming plugin deinstallation

Am kommenden Montag, den 16. März erfolgt die bereits mehrfach und seit längerem angekündigte Deinstallation der ILIAS-Erweiterungen Interaktives Video, Virtueller Meetingraum und ViPLab (Testfragentyp) als Vorbereitung auf das Upgrade auf ILIAS 10 am Montag, den 23. März. Bitte stellen Sie sich darauf ein, dass Objekte entsprechenden Typs endgültig aus dem System entfernt werden. Vgl. auch die Ankündigung auf der Anmeldeseite von ILIAS. | Next Monday, 16 March, the ILIAS extensions Interactive Video, Virtual Meeting Room and ViPLab (test question type) will be uninstalled, as announced several times and for some time now, in preparation for the upgrade to ILIAS 10 on Monday, 23 March. Please be aware that objects of the corresponding type will be permanently removed from the system. See also the announcement on the ILIAS login page.

Topological Quantum Many-Body Physics

Elective course on theory and applications of topological quantum phases.

General Information

Important Information
The goal of this course is to gain a thorough understanding of topological concepts in modern quantum many-body physics. You aquire the mathematical tools needed to describe topological quantum phases, understand the physical features that characterize these systems, and learn about potential applications.
Syllabus
Topological phases of non-interacting fermions:

- Integer quantum Hall effect
- Berry connection, Berry holonomy, Chern number
- Anomalous quantum Hall effect (Haldane model)
- Quantum spin Hall effect, topological insulators (Kane-Mele model)
- Pfaffian topological invariant
- Winding numbers, sublattice symmetry, edge modes (SSH model)
- Topological superconductivity (Majorana chain)
- Tenfold way and periodic table of topological insulators/superconductors
- Effects of interactions
- Topological bands in classical systems (topological metamaterials ...)

Symmetry-protected topological phases of interacting bosons:

- Tensor network states, matrix product states, PEPS
- Projective representations and (twisted) cohomology groups
- Classification of bosonic topological phases in one dimension
- Haldane chain and AKLT model

Intrinsic topological order and long-range entanglement:

- Statistics of indistinguishable particles in 2+1 dimensions (Braid group)
- Toric code (anyonic excitations, top. entanglement entropy ...)
- Topological quantum memories
- Fibonacci anyons
- String-net condensates
- Topological quantum computation (non-abelian anyons, braiding, fusion ...)
- Mathematical framework:
- Modular tensor categories, pentagon & hexagon relations,
- quantum dimension, topological spin ....
- Application to foundational questions of high-energy physics (fermions ...)
Target Group
M.Sc. Physik, M.Sc. Physics

Metadaten zur ECS-Freigabe

Dozent
Dr. Nicolai Lang
Veranstaltungstyp
Wahlpflichtmodul Ergänzung / Semicompulsory module
Ort
V57.05
SWS
4
Credits
9
Semester
SS25
Studiengänge
M.Sc. Physik, M.Sc. Physics

General

Language
English
Copyright
All rights reserved

Contact

Name
Nicolai Lang
Telephone
0711 685 65215
E-Mail
nicolai.lang@itp3.uni-stuttgart.de

Availability

Access
Unlimited
Admittance
You can join this course directly.
Registration Period
Unlimited
Period of Event
10. Apr 2025 - 18. Jul 2025

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Username
First Name
Last Name

Additional Information

Object-ID
5108520