IAS CMP/QFT Group Meeting

A Non-Semisimple Categorical Symmetry

Abstract: I will explain how to realize a gapped Hamiltonian for a (1+1)d system on the lattice which has a categorical symmetry given by the modules of the 4-dimensional Taft algebra. This category is finite but not a fusion category, a fact that presents two interesting physical features. First, we identify an S1-parametrised family of states that transform inequivalently under the non-semisimple symmetry. Second, we find a model where a product state and the so-called W state spontaneously break the symmetry. We will see how non-semisimplicity will offer a nice interpretation of why these two states are indistinguishable in the infinite-volume limit.

Date & Time

January 27, 2025 | 11:00am – 12:00pm

Location

Bloomberg Lecture Hall (IAS)

Speakers

Matthew Yu, University of Oxford

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