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 construct topological quantum field theories (TQFTs) and commuting projector
Hamiltonians for any 1+ 1d gapped phases with non-anomalous fusion category …

Two global symmetries are holoequivalent if their algebras of local symmetric operators are
isomorphic. A holoequivalent class of global symmetries is described by a topological order …

It has been a long-standing open problem to construct a general framework for relating the
spectra of dual theories to each other. Here, we solve this problem for the case of one …

We outline a holographic framework that attempts to unify Landau and beyond-Landau
paradigms of quantum phases and phase transitions. Leveraging a modern understanding …

Generalized symmetries often appear in the form of emergent symmetries in low energy
effective descriptions of quantum many-body systems. Noninvertible symmetries are a …

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

Originating from the topology of the path-integral target space $ Y $, solitonic symmetry
describes the conservation law of topological solitons and the selection rule of defect …

Topological holography is a holographic principle that describes the generalized global
symmetry of a local quantum system in terms of a topological order in one higher dimension …

We explore the rich landscape of higher-form and non-invertible symmetries that emerge at
low energies in generic ordered phases. Using that their charge is carried by homotopy …