We are currently witnessing rapid developments concerning the realization of quantum spin liquids in programmable quantum simulators and via Floquet engineering. Similarly, the realization of exotic fractonic phenomena in quantum spin liquids described by higher-rank gauge theories has now become possible in spin models with pursuits for their search in quantum materials. Over the past few years, we have achieved a deepened understanding of the problem of symmetry classification of quantum spin liquids relying on ideas and methods from category theory, and advanced notions in group theory. Substantial progress has also been made to understand the stability of gapless quantum spin liquids. Simultaneously, many-body numerical approaches based on neural network constructions, tensor network methods, and machine-learning approaches have allowed one to shed light on exploring quantum state preparation and its evolution.

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N. Perkins, University of Minnesota, USA

H. Pichler, University of Innsbruck, Austria

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