Exotic gapped boundaries of fracton phases in the Checkerboard model

Fracton topological order characterizes a new class of unconventional phases of matter and/or quantum error correcting codes. It involves exotic excitations with restricted mobility and ground-state degeneracy (GSD) growing with the size of the system. However, fracton models are often defined for infinite systems, and our understanding of their boundary theories is still incomplete. Here, we investigate possible boundaries for the Checkerboard model, a paradigmatic fracton model on the 3D cubic lattice. We focus on two cases: a horizontal boundary, along the (001) plane, and an oblique boundary, along the (111) plane, with periodic boundary conditions in the other directions. We discuss the GSD and the properties of boundary excitations (braiding statistics and boundary condensation) in these two cases. Finally, we discuss enforcing open boundary conditions in all directions, and the robustness of the GSD and of the logical qubits to such boundary conditions.