Exceptional-point-constrained locking of boundary-sensitive topological transitions in non-Hermitian lattices

Abstract: Point-gap topology under periodic boundary conditions and line-gap topology under open boundary conditions are generally inequivalent in non-Hermitian systems. We show that, in chiral non-Hermitian lattices, these two boundary-sensitive topological transitions become locked when the parameter sweep is confined to an exceptional-point (EP)-constrained manifold, such that the Bloch spectrum remains pinned to a zero-energy degeneracy throughout the evolution. In an extended non-Hermitian Su-Schrieffer-Heeger chain, this locking can be established analytically in a tractable limit, where the EP-constrained manifolds and the corresponding PBC and OBC transition boundaries are obtained in closed form, and it persists away from this limit when the generalized Brillouin zone is determined numerically. Outside the EP-constrained manifold, the two transitions generally decouple, even in the presence of isolated EPs or Hermitian degeneracies. We further show that the same mechanism survives in a four-band spinful extension with branch-resolved generalized Brillouin zones, including branch-imbalanced regimes. These results identify EP-constrained band evolution as a simple organizing principle for boundary-sensitive topology in chiral non-Hermitian systems and suggest a useful route for diagnosing non-Bloch topological transitions from periodic-boundary spectral evolution when such spectral information can be accessed in photonic, circuit, and cold-atom platforms.