Anisotropic layer construction of anisotropic fracton models

Abstract

We propose a coupled-layer construction of a class of fracton topological orders in three spatial dimensions, which has no immobile excitations but is characterized by single quasiparticle excitations constrained in one-dimensional subspaces and dipole excitations mobile in two-dimensional subspaces. The simplest model is obtained by stacking and coupling layers of the two-dimensional toric codes on the square lattice and can be exactly solved in the strong-coupling limit. The resulting subdimensional excitations are understood as a consequence of anyon pair condensation induced by the coupling between layers. We also present generalizations of the construction for layers of the Kitaev-honeycomb models, the ${Z}_{N}$ toric codes, and the toric codes and the doubled semion models on the honeycomb lattice.