Jie-Yu Zhang

Jie-Yu Zhang, Peng Ye

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.

Xiang-You Huang, Jie-Yu Zhang, Peng Ye

Lattice geometry profoundly shapes physical phenomena such as subsystem symmetry and directed percolation (DP). Among various lattice geometries, hyperbolic lattices are characterized by constant negative curvature and non-Abelian translation symmetry, offering a rich platform for investigating this geometry-physics interplay. However, the exponentially growing lattice size and nontrivial translation symmetry make approaches developed for Euclidean lattices incompatible, a limitation particularly evident in uniform cellular automata (CA). To resolve this, we develop a higher-order non-uniform cellular automata (NUCA) algorithm applicable to both translationally invariant regular Euclidean and hyperbolic lattices. In the algorithm, the non-uniform update rules incorporate nontrivial geometric data through a lattice-deforming procedure. We demonstrate the broad applicability of our algorithm to hyperbolic lattices through several applications on the hyperbolic $\{5,4\}$ lattice. By applying a linear NUCA, we generate subsystem symmetry-protected topological (SSPT) states and spontaneous subsystem symmetry-breaking states associated with regular or irregular subsystem symmetries unattainable on Euclidean lattices. We design the multi-point strange correlators to detect nontrivial SSPT states and derive a sufficient condition for non-Abelian translationally invariant NUCA-generated models. Furthermore, by generalizing the NUCA to non-uniform Clifford quantum cellular automata (CQCA), we generate subsystem symmetries of the hyperbolic cluster state, extending the established correspondence between translationally invariant CQCA and subsystem symmetries. Moreover, we simulate the DP process via a probabilistic NUCA that inherits the treelike structure of the lattice, and numerically estimate percolation thresholds and the phase diagram.