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 is characterized by spatially anisotropic mobility of quasiparticle excitations constrained in subdimensional manifolds. 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 fracton 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.