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This research investigates how quasiparticle mobility transforms under fusion rules within topological phases of matter enriched by subsystem symmetries. By constructing exactly solvable models, the authors demonstrate that restricted mobility classes obey distinct multi-channel fusion rules driven by deterministic geometric interference. The work advances fundamental understanding of anyonic statistics and transport constraints in quantum many-body systems with specific symmetry protections.
Fusion rules of mobility
arXiv:2508.13961v3 Announce Type: replace Abstract: 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 rules. We introduce three exactly solvable models with $\mathbb{Z}_2$ topological order enriched by subsystem symmetries to explicitly demonstrate these structures. Within these models, 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 multi-channel fusion rules. We present three explicit examples: (i) Fibonacci fusion rules; (ii) tensor products of Fibonacci rules; and (iii) lineon period transmutation.
Abstract: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 rules. We introduce three exactly solvable models with $\mathbb{Z}_2$ topological order enriched by subsystem symmetries to explicitly demonstrate these structures. Within these models, 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 multi-channel fusion rules. We present three explicit examples: (i) Fibonacci fusion rules; (ii) tensor products of Fibonacci rules; and (iii) lineon period transmutation.
Maintext+SM. published in PRB (2026) as a Letter. The other two works in this series are arXiv:2401.00505 [PRX Quantum 5, 030342 (2024)] and arXiv:2605.13379
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Formal Languages and Automata Theory (cs.FL)
arXiv:2508.13961 [quant-ph]
(or arXiv:2508.13961v3 [quant-ph] for this version)
Phys. Rev. B 114, L171107 (2026)
https://doi.org/10.1103/jrdw-vvct DOI(s) linking to related resources
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