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Explore arboreal quantum phases in this 47-minute conference talk delivered at the International Centre for Theoretical Sciences as part of the "Generalised symmetries and anomalies in quantum phases of matter" program. Delve into the fascinating intersection of quantum many-body systems and generalized symmetries, where traditional notions of symmetry are being revolutionized through higher-form, non-invertible, and subsystem symmetries. Discover how these new symmetry concepts provide powerful frameworks for understanding and classifying quantum phases of matter that extend beyond conventional paradigms. Learn about the role of anomalies in condensed matter physics and how they protect or constrain exotic quantum phases such as symmetry-protected topological states. Gain insights into how these developments are reshaping our understanding of quantum entanglement, conservation laws, and hydrodynamics in interacting systems, while also influencing perspectives on mixed states and open quantum systems. This presentation forms part of a comprehensive program designed to provide conceptual clarity for early-career researchers while promoting cutting-edge research in the rapidly evolving field of quantum matter and symmetry.
