Localization and topological transitions in non-Hermitian quasiperiodic lattices

We investigate the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-Andre-Harper model with irrational modulations in the off-diagonal hopping and on-site potential and with non-Hermiticities from the nonreciprocal hopping and complex potential phase. For noninteracting cases, we reveal that the nonreciprocal hopping (the complex potential phase) can enlarge the delocalization (localization) region in the phase diagrams spanned by two quasiperiodic modulation strengths. We show that the localization transition is always accompanied by a topological phase transition characterized the winding numbers of eigenenergies in three different non-Hermitian cases. Moreover, we find that a real-complex eigenenergy transition in the energy spectrum coincides with (occurs before) these two phase transitions in the nonreciprocal (complex potential) case, while the real-complex transition is absent with the coexistence of the two non-Hermiticities. For interacting spinless fermions, we demonstrate that the extended phase and the many-body localized phase can be identified by the entanglement entropy of eigenstates and the level statistics of complex eigenenergies. By making the critical scaling analysis, we further show that the many-body localization transition coincides with the real-complex transition and occurs before the topological transition in the nonreciprocal case, which are absent in the complex phase case.

Automated summary

In this study, localization and topological transitions in a one-dimensional non-Hermitian quasiperiodic lattice were investigated. The impact of nonreciprocal hopping, complex potential phase, and other non-Hermitian factors on the localization region in phase diagrams was revealed. It was found that the localization transition was accompanied by topological phase transitions characterized by winding numbers of eigenenergies, and a real-complex eigenenergy transition coincided with or occurred before these phase transitions in the nonreciprocal case. Additionally, the many-body localization transition was shown to coincide with the real-complex transition and precede the topological transition in the nonreciprocal case, with differences observed in the complex phase case.