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Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{\'e}-Fibonacci chain
- Source :
- Phys. Rev. B 104, 014202 (2021)
- Publication Year :
- 2021
-
Abstract
- In this paper, the interplay of the non-Herimiticity and the cascade of delocalization transition in the quasi-periodic chain is studied. The study is applied in a non-Hermitian interpolating Aubry-Andr{\'e}-Fibonacci (IAAF) model, which combines the non-Hermitian Aubry-Andr{\'e} (AA) model and the non-Hermitian Fibonacci model through a varying parameter, and the non-Hermiticity in this model is introduced by the non-reciprocal hopping. In the non-Hermitian AA limit, the system undergoes a delocalization transition by tuning the potential strength. At the critical point, the spatial distribution of the critical state shows a self-similar structure with the relative distance between the peaks being the Fibonacci sequence, and the finite-size scaling of the inverse participation ratios $({\rm IPRs})$ of the critical ground state with lattice size $L$ shows that ${\rm IPR}_g\propto L^{-0.1189}$. In the non-Hermitian Fibonacci limit, we find that the system is always in the extended phase. Along the continuous deformation from the non-Hermitian AA model into the non-Hermitian Fibonacci model in the IAAF model, the cascade of the delocalization transition is found, but only a few plateaux appear. Moreover, the self-similar structure of spatial distribution for the critical modes along the cascade transition is also found. In addition, we find that the delocalization transition and the real-complex transition for the excited states happen at almost the same parameter. Our results show that the non-Hermiticity provides an additional knob to control the cascade of the delocalization transition besides the on-site potential.
- Subjects :
- Condensed Matter - Disordered Systems and Neural Networks
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 104, 014202 (2021)
- Publication Type :
- Report
- Accession number :
- edsarx.2104.06035
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.104.014202