Coupled wire constructions of 3D topological phases

We present a general coupled wire construction in 3D in an effort to study novel topological phases of matter. Starting by stacking 1D quantum wires of free Dirac fermions into a rectangular array, interactions are added by introducing back scattering terms. The gapping terms are chosen to act on each plaquet of the array. By construction they mutually commute and hence completely gap out the bulk. The resulting theory is very rich, exhibiting many of the hallmarks of topological phases. We compute the ground state degeneracy on the 3 torus and study particular realizations which support fracton-like excitations.