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Explore non-invertible symmetries in lattice systems through this 52-minute conference talk delivered at the International Centre for Theoretical Sciences. Delve into the advanced concepts of generalized symmetries that extend beyond traditional notions in quantum many-body systems, focusing specifically on their implementation and behavior on discrete lattice structures. Learn how non-invertible symmetries represent a profound departure from conventional symmetry frameworks and discover their implications for understanding quantum phases of matter that fall outside standard classification schemes. Examine the mathematical foundations and physical manifestations of these exotic symmetries, including their role in protecting novel quantum states and their relationship to topological phases. Gain insights into cutting-edge research methodologies for studying non-invertible symmetries on lattices, including theoretical approaches and computational techniques. Understand how these symmetries connect to broader themes in modern condensed matter physics, such as quantum entanglement, conservation laws, and the classification of quantum phases. This presentation forms part of a comprehensive program on generalized symmetries and anomalies in quantum phases of matter, providing essential knowledge for researchers working at the intersection of high-energy physics concepts and condensed matter applications.
