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

TL;DR

This work develops lattice models exhibiting subsystem and weak non-invertible SPT order protected by non-group-like symmetries on Cub(d,p,q) graphs. By combining gauging, Kennedy-Tasaki transformations, and new non-invertible symmetry structures (notably Rep(D8)-like), the authors uncover robust interface and corner modes localized at codimension >1, and demonstrate anomalies such as type III and LSM-type mixed anomalies. They also establish duality-based distinctions among multiple SPT phases and explore how lattice translations enrich weak non-invertible SPT classifications, including explicit 2+1D constructions. The results advance the understanding of generalized symmetries in lattice systems, provide concrete realizations of higher-codimension protected modes, and point to symmetry-topological-field-theory formalisms for classifying these novel phases with potential implications for fracton-like orders and quantum information applications.

Abstract

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.

Figures (4)

• Figure 1: Several examples of $\mathbf{Cub}(d,p,q)$. Black and white dots indicate the vertices in $\mathbf{V}$ and $\mathbf{\Hat{V}}$, respectively.
• Figure 2: The $\alpha\beta$-interface in the case of $d=2$.
• Figure 3: The $\alpha\beta$-interface in the case of $d=2$.
• Figure 4: The $\alpha'\gamma$-interface $x_1 = 0$ for $\mathbf{Cub}(2,0,1)$.