Corner modes and ground-state degeneracy in models with gaugelike subsystem symmetries

Subsystem symmetries are intermediate between global and gauge symmetries. One can treat these symmetries either like global symmetries that act on subregions of a system, or gauge symmetries that act on the regions transverse to the regions acted upon by the symmetry. We show that this latter interpretation can lead to an understanding of global, topology-dependent features in systems with subsystem symmetries. We demonstrate this with an exactly solvable lattice model constructed from a two-dimensional system of bosons coupled to a vector field with a one-dimensional subsystem symmetry. The model is shown to host a robust ground-state degeneracy that depends on the spatial topology of the underlying manifold, and localized zero-energy modes on corners of the system. A continuum field theory description of these phenomena is derived in terms of an anisotropic, modified version of the Abelian K-matrix Chern-Simons field theory. We show that this continuum description can lead to geometric-type effects such as corner states and edge states whose character depends on the orientation of the edge.