Pseudo-Hermitian symmetry breaking and re-entrant localization in a one-dimensional non-Hermitian chain
Phys. Rev. A 113, 063736 – Published 26 June, 2026
DOI: https://doi.org/10.1103/7d49-jb7g
Abstract
Non-Hermitian systems have attracted considerable research interest due to their capacity to host unconventional physical phenomena. However, research on pseudo-Hermitian symmetry and re-entrant localization in one-dimensional non-Hermitian settings remain relatively limited. Here, we propose a one-dimensional non-Hermitian chain model composed of two coupled sublattices and investigate the effects of nonreciprocal hopping and quasiperiodic modulation on its physical properties. As the nonreciprocal hopping increases, the system undergoes a transition from a pseudo-Hermitian phase with entirely real energy spectra to a non-Hermitian phase characterized by the emergence of complex eigenenergies. Under a quasiperiodic potential, the system exhibits a rich phase diagram that includes extended, localized, and intermediate phases with mobility edges. Remarkably, we observe re-entrant localization, where the system switches nonmonotonically between extended and localized states as the potential strength or nonreciprocal hopping varies. This behavior originates from the synergy between quasiperiodicity-induced interference and the non-Hermitian skin effect. Dynamical analyses, such as wave-packet evolution, mean square displacement, and diffusion coefficients, further confirm these localization transitions. Our results underscore the essential role of nonreciprocal hopping in modulating topological and transport properties, offering valuable insights for the design of non-Hermitian quantum devices and sensors operating near exceptional points.
