Universität Wien

260050 VO Entanglement in quantum many-body systems (2024S)

5.00 ECTS (3.00 SWS), SPL 26 - Physik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Different from the information below, the course times are Thursday 14:45-16:15 and Friday 11:00-12:30 (in the Erwin Schrödinger lecture hall, as stated).

As described below ("Aims, contents and method of the course"), the course consists of two parts: The first part of the course is taught in the first half of the semester, at the times given above (i.e. 4 hours per week). In the second half of the semester, there is the option to choose one of two specializations (or both), which are taught in the Thursday and Friday slot, respectively.

Further details will be discussed during the course.

  • Friday 01.03. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 07.03. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 08.03. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 14.03. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 15.03. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 21.03. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 22.03. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 11.04. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 12.04. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 18.04. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 19.04. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 25.04. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 26.04. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 02.05. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 03.05. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 10.05. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 16.05. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 17.05. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 23.05. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 24.05. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 31.05. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 06.06. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 07.06. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 13.06. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 14.06. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Thursday 20.06. 14:45 - 16:15 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien
  • Friday 21.06. 11:00 - 11:45 Erwin-Schrödinger-Hörsaal, Boltzmanngasse 5, 5. Stk., 1090 Wien

Information

Aims, contents and method of the course

Complex quantum many-body systems exhibit a wide range of intriguing phenomena, which are rooted in their intricate quantum correlations: quantum entanglement. This includes e.g.

  • topological order, where systems order in their global quantum correlations, whereas this order is invisible in local properties; such systems can be used in quantum computers for robust quantum information storage;
  • measurement-based quantum computing, where the complex entanglement of a quantum many-body state can be used to carry out quantum computations solely by measurement
  • symmetry-protected order, where a seemingly trivial state acquires non-trivial properties due to the presence of a symmetry.

All these intricate and unconventional physical phenomena have their roots in the complex quantum entanglement present in those systems. At the same time, however, this entanglement makes these systems challenging to study, both analytically and numerically.

Fortunately, understanding the entanglement in these systems allows to settle this problem: Their entanglement structure gives rise to a succinct description, called tensor network states. Tensor network states precisely capture the complex entanglement which governs the behavior of such quantum many-body systems. This makes them both a powerful analytical tool to understand unconventional quantum matter, and a powerful ansatz for the numerical simulation of complex quantum many-body problems which are not susceptible to other methods due to their intricate quantum correlations.

This lecture provides a comprehensive introduction to tensor networks, with a focus on their use in modeling quantum many-body systems.

The lecture consists of two parts, which are given in the first and second half of the term, respectively.

The first part of the lecture gives a comprehensive introduction to the field of tensor networks. This includes an introduction to the key concepts, as well as the basics of both the analytical and the numerical use of tensor networks. The first part consists of 4h of lecture per week, i.e. both Thursday and Friday, and lasts for the first half of the semester (until early May).

For the second part of the lecture, there are two tracks. It is possible to either choose one track, or to take both tracks (see below). Each track consists of 2h of lecture per week, starting in the middle of the semester.

Track A: "Mathematical theory of tensor networks". This part specializes on mathematical aspects of tensor networks. This in particular covers the use of tensor networks in the classification of exotic phases with topological order, and their representation theory. The topics in this specialization are mostly algebraic.

Track B: "Numerical simulations with tensor networks". This part gives a detailed introduction to the different use of tensor networks for the numerical simulations of quantum many-body systems, as well as problems in statistical mechanics, in one, two and three dimensions. This track in particular also includes hands-on programming exercises.

Unless agreed otherwise, Track A is held in the Friday slot, and Track B is held in the Thursday slot, both starting at the middle of the semester. Students who attend one of the tracks can earn ECTS points for this course [260050 VO Entanglement in quantum many-body systems (2024S)]. Students who wish to attend both tracks can additionally earn ECTS points for the course https://ufind.univie.ac.at/de/course.html?lv=250068&semester=2024S

The lecture is taught jointly by Norbert Schuch (Faculty of Physics and Faculty of Mathematics), José Garre Rubio and András Molnár (Faculty of Mathematics), and Bram Vanhecke (Faculty of Physics).

For further information, see the lecture's website at https://schuch.univie.ac.at/nschuch/ent-qmb-ss24/

Assessment and permitted materials

The exam will be conducted as an oral exam of 30 minutes. The exam will cover the material taught in the first part of the course, together with the material taught either in specialization Track A or Track B. Students who wish to take both tracks will be examined on both tracks (exam time of 40 minutes), and additionally earn ECTS points for course 250068 "Entanglement in quantum many-body systems: Mathematical results": https://ufind.univie.ac.at/de/course.html?lv=250068&semester=2024S

Important: Beyond the exam dates indicated in u:find, there is also the possibility to make individual appointments for exams. It is recommended that students interested in taking the exam, contact Prof. Schuch (norbert.schuch@univie.ac.at) prior to registering for the exam to discuss the date and time of the exam.

Minimum requirements and assessment criteria

Students must demonstrate knowledge of the topics covered in the first part of the lecture, as well as in the chosen specialization of Track A or Track B. The exam will both include questions testing the knowledge of the material, and its application to concrete examples, such as the properties of specific tensor network models.

Examination topics

The exam will cover the entire material taught in the course, as published on the course website on https://schuch.univie.ac.at/nschuch/ent-qmb-ss24/. Alternatively, the material covered in the reading list can be examined.

Reading list

For the first part of the lecture: https://arxiv.org/abs/1603.03039
For Track A: https://arxiv.org/abs/2011.12127
For Track B: https://arxiv.org/abs/1611.08519

Association in the course directory

M-VAF A 2, M-VAF B, PM-SPEC

Last modified: Tu 27.08.2024 13:46