Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-André-Fibonacci chain

In this paper, the interplay of non-Herimiticity and cascade delocalization transition in quasi-periodic chain is studied. The study applied a non-Hermitian interpolating Aubry-Andr{\'e}-Fibonacci (IAAF) model, which combines Aubry-Andr{\'e} (AA) model Fibonacci through varying parameter, non-Hermiticity introduced by non-reciprocal hopping. AA limit, system undergoes tuning potential strength. At critical point, spatial distribution state shows self-similar structure with relative distance between peaks being sequence, finite-size scaling inverse participation ratios $({\rm IPRs})$ ground lattice size $L$ that ${\rm IPR}_g\propto L^{-0.1189}$. we find always extended phase. Along continuous deformation from into IAAF found, but only few plateaux appear. Moreover, for modes along also found. addition, real-complex excited states happen at almost same parameter. Our results show provides an additional knob to control besides on-site potential.