Speaker
Description
I will present a construction of a family of 1D quantum lattice models with unitary fusion category symmetry. These models generalize the well-known anyon chain construction and can be viewed as edge theories of 2D symmetry-enriched topological states. They realize a variety of interesting phases, including gapless critical phases and phases with spontaneously broken categorical symmetries. A particularly interesting phase is an antiferromagnet-like phase in which both translation and category symmetry are broken but certain combined symmetries remain intact. However, it differs fundamentally from the conventional antiferromagnet because the associated magnetic domain walls are non-invertible. I will also briefly discuss the representative phase transitions, including gapped-to-gapless or gapless-to-gapless transitions.