Non-invertible Symmetry protected topological phases in higher dimensions

In this talk, we construct lattice models of non-invertible symmetry-protected topological (NISPT) phases in higher dimensions and use strange correlators (and related diagnostics) to distinguish them. Moving beyond 1+1D, higher-dimensional NISPTs remain poorly charted: mathematical descriptions are incomplete; higher-form and non-invertible symmetries often coexist; and regular tensor-network realizations are scarce and technically demanding. In 2+1D, we employ ZX-calculus to reproduce prior results and then extend the lattice construction to a broader family of NISPT phases, for which we explicitly construct the strange correlators. In 3+1D, we construct lattice models realizing a Zn*Zn 1-form SPT and identify a class of NISPT phases invariant under the gauging map. Our results show that explicit lattice constructions with ZX-calculus enable phase discrimination and data extraction where standard constructions are limited—offering clues to other more general theories.