Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry

Abstract: Spatially modulated symmetries have emerged since the discovery of fractons, which characterize unconventional topological phases with mobility-constrained quasiparticle excitations. On the other hand, non-invertible duality defects have attracted substantial attention in communities of high energy and condensed matter physics due to their deep insight into quantum anomalies and exotic phases of matter. However, the connection between these exotic symmetries and defects has not been fully explored. In this paper, we construct concrete lattice models with non-invertible duality defects via gauging spatially modulated symmetries and investigate their exotic fusion rules. Specifically, we construct spin models with subsystem symmetries or dipole symmetries on one, two, and three-dimensional lattices. Gauging subsystem symmetries leads to non-invertible duality defects whose fusion rules involve $0$-form subsystem charges in two dimensions and higher-form operators that correspond to ``lineon'' excitations (excitations which are mobile along one-dimensional line) in three dimensions. Gauging dipole symmetries leads to non-invertible duality defects with dipole algebras that describe a hierarchical structure between global and dipole charges. Notably, the hierarchical structure of the dual dipole charges is inverted compared with the original ones. Our work provides a unified and systematic analytical framework for constructing exotic duality defects by gauging relevant symmetries.