# Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries

## TL;DR

This paper explores models with subsystem symmetries, revealing topological ground-state degeneracy and corner modes, using an exactly-solvable lattice model and a continuum field theory approach.

## Contribution

It introduces a new understanding of subsystem symmetries as gauge-like, demonstrating topology-dependent features and corner states in a novel lattice model and continuum theory.

## Key findings

- Ground state degeneracy depends on manifold topology
- Presence of localized zero-energy corner modes
- Continuum field theory captures geometric effects

## Abstract

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 2D system of bosons coupled to a vector field with a 1D 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.