Simple anisotropic three-dimensional quantum spin liquid with fractonlike topological order

International audienceWe present a three-dimensional cubic lattice spin model, anisotropic in the ẑ direction, that exhibits fractonlike order. This order can be thought of as the result of interplay between two-dimensional Z2 topological order and spontaneous symmetry breaking along the ẑ direction. Fracton order is a novel type of topological order characterized by the presence of immobile pointlike excitations, named fractons, residing at the corners of an operator with two-dimensional support. As other recent fracton models, ours exhibits a subextensive ground-state degeneracy: On an Lx×Ly×Lz three-torus, it has a 22Lz topological degeneracy and an additional symmetry-breaking nontopological degeneracy equal to 2LxLy−2. The fractons can be combined into composite excitations that move either in a straight line along the ẑ direction or freely in the xy plane at a given height z. 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. We find zero energy modes on the surfaces perpendicular to either the x̂ or ŷ directions and their absence on the surfaces normal to ẑ. This result can be explained using the properties of the two kinds of composite two-fracton mobile excitations