Tensor Network Based Approaches to Quantum Many-Body Systems

Tensor networks provide a new paradigm for describing quantum many body systems. Since the early years of quantum mechanics, the quantum many body problem has been one of the main driving forces in theoretical physics. In the last 25 years, the important role of entanglement in the study of these systems has become increasingly clear, giving rise to an interdisciplinary research effort at the boundary of entanglement theory and many-body physics. It has motivated the study of tensor networks, which model the entanglement structure of a system through local tensors, thereby reconciling global entanglement with a local description. This has led to the development of new numerical methods for simulating complex quantum systems in and out of equilibrium, as well as to the discovery of new analytic tools for classifying topological phases of matter. The field has been steadily growing in recent years, with an increasing range of numerical methods and analytical concepts being developed, and connections to other fields such as high-energy physics or quantum gravity being explored.

The goal of this school is to provide new students entering the field with an in-depth introduction to the fast-moving field of tensor networks, covering basic concepts, their numerical use, and their analytical utility, as well as to get them in contact with some of the most relevant recent developments in the field. Furthermore, the school serves as a platform for the students to get to know each other and to foster collaborations, which is particularly important given the increasing number of groups working on the topic.

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