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

ABSTRACT

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 investigated. In the symmetry‐unbroken regime, energy eigenvalue arguments are constrained to two discrete values separated by . To characterize topology beyond this spectral constraint, a new pseudo‐anyonic‐Hermiticity (PAH) symmetry is introduced as the topological protecting symmetry for anyonic‐PT‐symmetric systems. For a representative dimer lattice, edge states reside in a complex line gap and exhibit a constrained energy phase in symmetry‐unbroken regime, which serves as a signature of topological protection. Our results reveal the energy phase constraint property and define a new non‐Hermitian topological phase through the PAH symmetry. This work broadens the conceptual foundation of topological protection under generalized non‐Hermitian symmetries.