Twisted Fracton Models in Three Dimensions

Right now great interests are growing among physicists on a new possibility of quantum phases which support immobile quasiparticles, so-called fractons. Most currently studied fracton models in three dimensions can be viewed as generalized abelian gauge theories. By analogy to Dijkgraaf-Witten topological gauge theories, we notice a simple further generalization of these models by twisting. Based on this observation, we construct a larger family of exactly solvable models, which we dub twisted fracton models. To characterize the corresponding quantum phases, we study their ground state degeneracy under periodic boundary conditions and the topological properties of their quasiparticles. In particular, we see a simple realization of non-abelian fractons.