Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders

Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. While these exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, they are not capable of describing those with chiral gapless surface states. Based on cellular construction recently proposed for 3d topological phases, we introduce a systematic way to produce another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that they can describe both 3d topological and fracton orders and even their hybrid and study their universal features such as quasiparticle statistics and topological ground-state degeneracy. As a byproduct, we apply this construction to two-dimensional coupled-wire models with ordinary topological orders and translation symmetry enriched topological orders. We believe that our results pave the way to investigate effective quantum field descriptions or microscopic model realizations of fracton orders with chiral gapless surface states.