Lattice models with subsystem/weak non-invertible symmetry-protected topological order

We construct a family of lattice models which possess subsystem non-invertible symmetry-protected topological (SPT) order and analyze their interface modes protected by the symmetry, whose codimension turns out to be more than one. We also propose 2+1d lattice models which belong to two different weak SPT phases distinguished by a combination of translational symmetry and non-invertible symmetry. We show that the interface between them exhibits an exotic Lieb-Schultz-Mattis (LSM) anomaly associated with a modulated symmetry, which cannot be factorized into a direct product of internal and translational symmetries.