250148 VO Mathematical Aspects of Tensor Networks in Many-Body Physics (2023S)

Important note: This course is intended as part of the course https://ufind.univie.ac.at/de/course.html?lv=260061&semester=2023S "Tensor network methods in many-body physics". -- Further information on the course and the format can be found there, or on the course website https://schuch.univie.ac.at/nschuch/tensornetworks-ss23/

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Tensor networks are a powerful framework for the study of many body-systems. Most importantly, they form the right language to study quantum many-body systems, both analytically and numerically. This in particular includes systems which exhibit exotic types of order (so-called "topological order"), which cannot be described by the standard framework of symmetry breaking and local order parameters, as well as other types of systems where quantum correlations play an important role.

The key reason for their success is that tensor networks are precisely built to capture the complex entanglement (i.e., the quantum correlation) which govern the behavior of such quantum many-body systems. On the one hand, this makes tensor networks a powerful tool to analytically understand and characterize the different unconventional phases and to build exactly solvable models. On the other hand, it also makes them 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.

Beyond that, tensor networks also naturally appear in the description of problems in classical statistical mechanics, where they give rise to extremely accurate numerical methods, as well as e.g. in the modeling of high-dimensional data.

This lecture is offered in combination with the course

https://ufind.univie.ac.at/de/course.html?lv=260061&semester=2023S

"Tensor network methods in many-body physics"

This course consists of two parts, which are given in the first and second half of the term, respectively. The first part will provide a general introduction to the topic. The second part will consists of two tracks, Track A: "Mathematical theory of tensor networks", and Track B: "Numerical simulations with tensor networks".

In the second part it will be possible either specialize on one of the tracks, or to take both tracks.

Students interested in only one track will earn ECTS points for the course 260061 "Tensor network methods in many-body physics". More information on the course can be found at https://ufind.univie.ac.at/de/course.html?lv=260061&semester=2023S

Students who take both specialization tracks will also earn points for this course.