250068 VO Entanglement in quantum many-body systems: Mathematical results (2024S)

Important note: This course is intended as part of the course https://ufind.univie.ac.at/de/course.html?lv=260050&semester=2024S "Entanglement in quantum many-body systems".
Further information on the course and the format can be found there, or on the course website: https://schuch.univie.ac.at/nschuch/ent-qmb-ss24/

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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 statesprecisely 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.

This lecture is offered in combination with the course 260050 VO Entanglement in quantum many-body systems (2024S): https://ufind.univie.ac.at/de/course.html?lv=260050&semester=2024S

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

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

Students interested in only one track can earn ECTS points for the course 260050 "Entanglement in quantum many-body systems". More information on the course can be found at https://ufind.univie.ac.at/de/course.html?lv=260050&semester=2024S

Students who take both specialization tracks can also earn points for this course [250068 VO Entanglement in quantum many-body systems: Mathematical results (2024S)]