Description
Hilbert spaces of chains of non-Abelian anyons are constrained by their fusion rules. These constraints may restrict the dynamics and lead to nontrivial thermalization behavior for such systems. As an examplary anyonic model with restricted thermalization, we suggest a one dimensional Fibonacci anyonic chain where the topological charges can perform braid moves around each other. We identify subspaces in the fusion space of this model which are left invariant by certain braid moves and by fine-tuning an additional magnetic field, we find various dynamically disconnected sectors. These sectors stem from the destructive interference of different braid processes and we expect that this model displays weak Hilbert space fragmentation. Moreover, we show that in global quenches certain initial states do not evolve to thermal states but display fidelity revivals up to late times.
