Anomalous spectrum in a non-Hermitian quasiperiodic chain

The spectra of particles in disordered lattices can either be completely extended or localized or can be intermediate, which hosts both the localized and extended states separated from each other. In this work, however, we show that in the case of a one-dimensional lattice with long-range hopping and non-Hermitian quasiperiodic on-site potential, the localized and extended states in the spectrum are intermixed with each other rather than well separated. As a result, an atypical intermediate phase appears where extended states intermittently appear in the pool of localized states. We also argue that such anomalous spectral intermixing can be realized in the short-range hopping limit by appropriate engineering of the on-site potential. Moreover, we obtain that the nature of the spectrum also reveals nonstandard scenarios in the complex energy plane where the complex energies encircle real ones. These findings shed light on the intricate interplay between the non-Hermiticity and quasiperiodic disorder in the system.