Spontaneously Broken Non-Invertible Symmetries in Transverse-Field Ising Qudit Chains with Kristian Tyan Kai Chung

Symmetries are powerful tools which place strong constraints on physical systems. Classifications of phases of matter are based on patterns of symmetry-protected topology (SPT) and spontaneous symmetry-breaking (SSB). The past decade has seen the rapid formalization and development of the “generalized symmetries” paradigm, which broadens our conception of symmetries in a variety of directions: higher-form, spatially modulated, and non-invertible. Based on recent work [arxiv:2508.11003], I will discuss the non-invertible aspect using simple 1D toy models based on finite groups which host so-called Rep(G) symmetry. These models are direct generalizations of the transverse-field Ising model and provide a simple platform to juxtapose invertible and non-invertible symmetry breaking. I will show that non-invertible symmetry broken states exhibit features characteristic of both invertible SSB and SPT phases, along with characteristics which are not realizable by invertible symmetries. I will comment on the connection to non-Abelian lattice gauge theory, where Wilson loops furnish an analogous 1-form Rep(G) symmetry.