A Non-Semisimple Categorical Symmetry

Watch a physics lecture from the Institute for Advanced Study where Matthew Yu from the University of Oxford explores the realization of a gapped Hamiltonian for a (1+1)d system on the lattice with categorical symmetry defined by the modules of the 4-dimensional Taft algebra. Delve into the unique properties of this finite but non-fusion category, examining two key physical features: an S1-parametrised family of states with inequivalent transformations under non-semisimple symmetry, and a model demonstrating spontaneous symmetry breaking through both product and W states. Learn how non-semisimplicity provides insight into the indistinguishability of these states in the infinite-volume limit.