Speaker: Kansei Inamura (Oxford)
Title: Non-invertible symmetries on a tensor product Hilbert space in 1+1 dimensions
Abstract: I will introduce an index of non-invertible symmetry operators in 1+1 dimensions and discuss its relation to the realizability of non-invertible symmetries on the tensor product of finite dimensional on-site Hilbert spaces on the lattice. Our index generalizes the Gross-Nesme-Vogts-Werner index of quantum cellular automata (QCAs). Assuming that all fusion channels have the same index, I will show that the fusion rules of finitely many symmetry operators on a tensor product Hilbert space can agree, up to QCAs, only with those of weakly integral fusion categories. This result generalizes a recent mathematical result obtained by Evans and Jones and supports a physical conjecture by Tantivasadakarn.