Symmetry-Engineered Multiple Bulk-Boundary Correspondences and Anomalous Modes in a Non-Hermitian Creutz Ladder

Abstract

The synergy between non-Hermiticity and topology makes the bulk-boundary correspondence (BBC) highly elusive. Here we study a non-Hermitian Creutz ladder incorporating both gain-loss and nonreciprocity, and construct multiple BBCs involving scale-free, normal and anomalous skin modes, as well as topological zero- energy modes. We characterize the skin effect induced by the parity-time (PT) phase transition through an average winding number, thereby formulating PT-related BBC. Furthermore, a hidden chiral symmetry ensures that topological phase transitions can be reliably detected via a Z 2 invariant. Although the gain-loss breaks the standalone P symmetry, it preserves the combined PT symmetry, allowing a modified Z 2 invariant to sustain the topological BBC. Notably, sublattice symmetry facilitates the precise analytical determination of non-Bloch spectra. Leveraging this, we introduce a hybrid spectral winding that encodes the localization (or delocalization) characteristics of two counterintuitive bulk modes coexisting with normal skin modes, thus defining a non- Hermitian BBC. One of these modes exhibits exponential boundary accumulation in a direction opposite to the nonreciprocity, while the other manifests as an anomalous surge of Bloch-wave states within the nonreciprocal lattice. These results reveal a series of unexpected phenomena governed by underlying symmetry, significantly broadening our fundamental understanding of the BBC mechanism in non-Hermitian topological systems.