We propose a general framework to characterize gapped infra-red (IR) phases of theories
with non-invertible (or categorical) symmetries. In this paper we focus on (1+ 1) d gapped …

We present a general approach for detecting when a fusion category symmetry is
anomalous, based on the existence of a special kind of Lagrangian algebra of the …

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+ 1d lattice models on a
tensor product Hilbert space of qubits. This symmetry is associated with a topological defect …

We explore exact generalized symmetries in the standard 2+ 1d lattice $\mathbb {Z} _2 $
gauge theory coupled to the Ising model, and compare them with their continuum field …

Abstract We construct (2+ 1)-dimensional lattice systems, which we call fusion surface
models. These models have finite non-invertible symmetries described by general fusion 2 …

A bstract We discuss the fermionization of fusion category symmetries in two-dimensional
topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is …

Despite growing interest in beyond-group symmetries in quantum condensed matter
systems, there are relatively few microscopic lattice models explicitly realizing these …

We provide a generalization of the Symmetry Topological Field Theory (SymTFT) framework
to characterize phase transitions and gapless phases with categorical symmetries. The …

Non-invertible categorical symmetries have emerged as a powerful tool to uncover new
beyond-Landau phases of matter, both gapped and gapless, along with second order phase …

We consider symmetry protected topological (SPT) phases with finite non-invertible
symmetry $\mathcal {C} $ in 1+ 1d. In particular, we investigate interfaces and …