Fusion Rules of Mobility
This work provides a new theoretical framework for understanding how mobility constraints combine in topological phases, relevant for condensed matter physicists studying anyonic systems and fracton phases.
The paper reveals that restricted mobility classes in topological phases obey complex multi-channel fusion algebras, demonstrated via exactly solvable models with Z2 topological order enriched by subsystem symmetries. Three explicit mobility fusion phenomena are realized: Fibonacci fusion rules, tensor products of Fibonacci rules, and lineon period transmutation.
In topological phases of matter, fusion rules dictate how anyonic topological charges combine. However, the transformation of quasiparticle mobility under fusion remains largely unexplored. In this letter, we reveal that restricted mobility classes obey their own complex multi-channel fusion algebras. We introduce a family of exactly solvable models with $\mathbb{Z}_2$ topological order enriched by subsystem symmetries to explicitly demonstrate these structures. Within this framework, mobility constraints arise from enforcing symmetries supported on specific subsets. When excitations fuse, these rigid geometric constraints interfere spatially. At the macroscopic level, this deterministic geometric interference manifests as a multi-channel fusion ring. We present three explicit mobility fusion phenomena realized in distinct models: (i) Fibonacci fusion rules; (ii) tensor products of Fibonacci rules; and (iii) lineon period transmutation.