Localization and topological transitions in non-Hermitian quasiperiodic lattices

TL;DR

This paper explores how non-Hermitian quasiperiodic lattices exhibit localization, topological transitions, and real-complex eigenenergy changes, revealing their interrelations and effects on many-body localization in interacting systems.

Contribution

It uncovers the interplay between non-Hermitian effects, localization, and topology in quasiperiodic lattices, including the relation between real-complex and topological transitions.

Findings

Nonreciprocal hopping enlarges delocalization regions.

Localization transitions coincide with topological phase transitions.

Many-body localization aligns with real-complex eigenenergy transitions.

Abstract

We investigate the localization and topological transitions in a one-dimensional (interacting) non-Hermitian quasiperiodic lattice, which is described by a generalized Aubry-Andr\'{e}-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 quasiperiodical modulation strengths. We show that the localization transition are 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 under 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.