Gauging fractons: Immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies

Fracton phases of matter contain quasiparticles that are constrained, not by energetics but by the structure of local operators, to move along lower dimensional submanifolds. Here, the authors present a very general scheme for producing exactly solvable, non-Abelian fracton models by gauging symmetries that permute fractons, exploring several examples in detail. One of the resulting models contains immobile, non-Abelian quasiparticles that can only be created at the corners of operators with fractal support.