Phase transitions in non-Hermitian superlattices

We investigate the energy spectral phase transitions arising in one-dimensional superlattices under an imagi-nary gauge field and possessing M sites in each unit cell in the large M limit. It is shown that in models displaying nearly flat bands, a smooth phase transition, from quasi-entirely-real to complex energies, can be observed as the imaginary gauge field is increased, and that the phase transition becomes sharper and sharper (exact) as M is increased. In this limiting case, for superlattices with random or incommensurate disorder, the spectral phase transition corresponds to a localization-delocalization transition of the eigenfunctions within each unit cell, dubbed non-Hermitian delocalization transition and originally predicted by Hatano and Nelson [N. Hatano and D. R. Nelson, Phys. Rev. Lett. 77, 570 (1996)]. However, it is shown here that in superlattices without disorder, a spectral phase transition can be observed as well, which does not correspond to a non-Hermitian delocalization phase transition. The predicted phenomena could be observed in non-Hermitian photonic quantum walks, where synthetic superlattices with controllable M and imaginary gauge fields can be realized with existing experimental apparatus.

Automated summary

We investigate the energy spectral phase transitions in one-dimensional superlattices with M sites and an imaginary gauge field. It is found that in models with nearly flat bands, a smooth phase transition from real to complex energies can be observed as the imaginary gauge field increases, becoming sharper with increasing M. This phase transition can be observed even in superlattices without disorder. These predicted phenomena can be realized in non-Hermitian photonic quantum walks using existing experimental apparatus.