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X-cube model on generic lattices: Fracton phases and geometric order

The authors present a generic lattice construction for a generalized X-cube model of fracton topological order and propose a coarser definition of phase of matter for fracton orders. Similar to other fracton models, this model hosts emergent subdimensional excitations, which are topologically robust excitations that are confined to only move along certain lines or surfaces. The model is constructed from stacks of intersecting surfaces, and the subdimensional excitations are confined to move only along these (possibly curved) surfaces or their intersections. Surprisingly, for certain curved intersecting surfaces, a robust ground-state degeneracy on a manifold with trivial topology can result.