Spectra, eigenstates and transport properties of a PT-symmetric ring

We study, analytically and numerically, a simple PT-symmetric tight-binding ring with an onsite energy a at the gain and loss sites. We show that if a not equal 0, the system generically exhibits an unbroken PT-symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points (EPs), there are 'diabolical points', and inverse EPs at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary 'backflow' of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.

Automated summary

In this study, a simple PT-symmetric tight-binding ring with an onsite energy is investigated analytically and numerically. It is found that the system exhibits an unbroken PT-symmetric phase if the onsite energy is nonzero. The spectrum is characterized by singularities in the complex parameter space and the behavior of eigenstates at large gain and loss strengths. Additionally, the transport properties of the system are studied, revealing the occurrence of backflow of density and the existence of singular eigenstates that do not depend on the strength of gain and loss.