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## Topological phases in condensed matter and cold atom systems

#### Institut d'Etude Scientifique de Cargese (IESC), France

#### Organisers

The 2016 Nobel Prize in Physics was awarded to pioneering work opening the field of topological phases of matter. This field has matured later on in the study of the fractional quantum Hall effect, which continues to deliver exciting physics, in the form of non-abelian excitations and the observation of neutral edge modes. Inspired by the quantum Hall effect, the study of non-abelian particles has branched into different topics, such as the study of topological phases emerging in (spin) lattice models and recently topological insulators and superconductors. During recent years, the field of topological phases has been boosted by the possible application to quantum computing. Implementing topological quantum computation in realistic experimental systems is one of the holy grails of the community.

Most notable are the newly discovered topological insulators (or superconductors), which combine physics from the quantum Hall effect and graphene. Currently, most of the interesting physics in topological insulators emerges from combining non-interacting band theory with the notion of topology, which has led to some spectacular results. However, the fact that most of the developments in the field of topological insulators have focused on the effects of the topological properties alone means that consideration of the consequences of adding electron interactions are largely missing. While the latter give rise to very interesting physics in their own right, combining them with topological structures will most certainly lead to many interesting discoveries. The fractional quantum Hall effect is a prime example of where this interplay indeed has led to very exciting new physics. Classifying topological phases in the presence of interactions is a daunting task, so that making even a little progress will greatly enhance our understanding of topological phases. This is one of the main questions that will be be addressed during the workshop.

It is worth emphasizing the dynamism that the field has received through the development of NISQ processors. It is just now becoming feasible to emulate/simulate a wide variety of many-body phases -- both static and dynamic properties -- using these near term quantum computing platforms, with new non-equilibrium topological properties -- such as various types of Floquet insulators -- being of particular interest.

## References

**France**

Didier Poilblanc (Laboratoire de Physique ThÃ©orique) - Organiser

Nicolas Regnault (ENS/CNRS/Princeton University) - Organiser

**Germany**

Roderich Moessner (MPIPKS) - Organiser