A Simple Anisotropic Three-dimensional Quantum Spin Liquid with Fracton Topological Order

Fracton phases are one of the latest developments in three-dimensional topological order. Characterized by the presence of immobile pointlike excitations, named fractons, these phases exhibit subextensive topological degeneracy. We present an anisotropic three-dimensional cubic lattice spin model, that exhibits fracton topological order. In addition to the topological degeneracy that is exponential in the system's length, our model displays ground state degeneracy, that can be lifted locally. The latter is exponential in the system's surface area. The fractons can be combined into composite excitations that move either in a straight line along the anisotropic direction, or freely in the plane perpendicular to it. While our model draws inspiration from the toric code, we demonstrate that it cannot be adiabatically connected to a layered toric code construction. Additionally, we investigate the effects of imposing open boundary conditions on our system.