Searching for Symmetry: From Quantum Groups to Strong Zero Modes

Locality restricts the kinds of symmetries that can be realized in physical systems. In this talk, we will present the results of a systematic search for a broad class of symmetries that can be realized in simple spin-1/2 models, which can be performed using the framework of commutant algebras for understanding symmetries. This reveals a rich landscape of realizable symmetries. While some are fairly conventional, such as Z2, U(1), and SU(2), we find many unconventional ones, such as quantum group symmetries, quantum many-body scars, and Strong Zero Modes (SZMs). Crucially, this understanding of SZMs allows the construction of non-integrable models that possess exact SZMs, which were earlier thought to occur exactly only in the presence of integrability. This exploration shows that novel symmetries and dynamical phenomena can in principle be discovered using such "blind" searches.