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Phase Transitions and Topological Protection in Anyonic-PT-Symmetric Lattices

Parity-time (PT) symmetry and anti-PT symmetry have attracted extensive interest for their non-Hermitian spectral properties, particularly the emergence of purely real and imaginary eigenvalues in their symmetry-unbroken regime, respectively. Recently, these two scenarios have been unified under a more general framework known as anyonic-PT symmetry, yet its physical implications in waveguide platforms and corresponding topological features in extended lattice systems remain largely unexplored. Here, the phase transitions and topological protection in anyonic-PT-symmetric systems are systematically investigated in waveguide lattices. In the symmetry-unbroken regime, the arguments of all bulk eigenvalues are constrained to two discrete values separated by π, leading to distinctive oscillatory propagation dynamics accompanied by controlled amplification or dissipation. In the case of one-dimensional lattice, the energy bands exhibit a gap closing and reopening during phase transition. Moreover, in the symmetry-unbroken regime, the topological edge states emerge within the bulk gap and are protected by a generalized pseudo-anyonic-Hermiticity (PAH) symmetry. Our results establish anyonic-PT symmetry as a new tunable degree of freedom for non-Hermitian waveguide systems, where the eigenvalue argument provides a natural quantity for information encoding. This work broadens the conceptual foundation of topological protection under generalized non-Hermitian symmetries.