Non-Abelian anyons are the quasiparticles with fascinating properties in two-dimensional topological phases of matter, which are candidates for fault-tolerant quantum computation. Beyond the traditional type of topological phases, fracton orders in three dimensions have the unique feature that some excitations are immobile, making them suitable for quantum memories. Non-Abelian fractons combine the two features above, and are important subjects for theoretical developments and potential applications to quantum information science. However, due to lack of a generic mathematical description of the non-Abelian fractions, a systematical construction of the lattice model is desired. Here, we develop a novel way to construct non-Abelian fractons on lattices based on the gauging principle.

The principle of gauging has a tremendous success in obtaining several topological phases of matters. In electromagnetism, one can start from the symmetry of a matter field, construct the gauge potentials and the gauge transformation, and finally obtain the properties of the electric charge and the magnetic flux. Now, we generalize the construction by starting from a matter field having exotic symmetries, and find that the resulting “electric charges” and “magnetic fluxes” contain non-Abelian fractons. Moreover, we find that, under certain conditions, the algebraic properties of those charges and fluxes are the same as their counterparts in two-dimensional lattice gauge theory for non-Abelian anyons.

Our construction using the gauging principle makes the identification of species and properties of fractons more straightforward. In particular, the correspondence between fractons and anyons from the algebtric structure sheds light on classifying fracton orders.