A Non-Semisimple Categorical Symmetry on the LatticeConfirmed

by Matthew Yu (University of Oxford - Mathematical Institute)

Friday May 8, 2026, 2:30 PM → 4:00 PM America/Toronto

PI/3-394 - Skyroom (Perimeter Institute for Theoretical Physics)

Semisimple categorical symmetries, and their physical implications have been studied in great detail in the continuum and on the lattice. In particular, the nice properties of semisimple categories allows one to construct hamiltonians which enjoy this symmetry, and study its symmetric gapped phases. Using the anyonic chain framework in (1+1)d, I will present a model that has a finite but non-semisimple categorical symmetry. Sacrificing Hermiticity, I will present several symmetric, frustration-free, gapped Hamiltonians with real spectra and analyze their ground state subspaces. I then discuss two intriguing phenomena. First, I will identify a smooth path of gapped symmetric Hamiltonians whose ground states transform inequivalently under the symmetry. Second, I will discuss a model where a product state and the so-called W state spontaneously break the symmetry, and propose an explanation for the indistinguishability of these two states in the infinite-volume limit in terms of the symmetry category.