Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals

Abstract

In this paper, a non-Hermitian Aubry-André-Harper model with power-law hoppings ($1/s^a$) and quasiperiodic parameter $\beta$ is studied, where $a$ is the power-law index, $s$ is the hopping distance, and $\beta$ is a member of the metallic mean family. We find that under the weak non-Hermitian effect, there preserves $P_{\ell =1,2,3,4}$ regimes where the fraction of ergodic eigenstates is $\beta$-dependent as ${\beta }^{\ell }$L ($L$ is the system size) similar to those in the Hermitian case. However, $P_{\ell }$ regimes are ruined by the strong non-Hermitian effect. Moreover, by analyzing the fractal dimension, we find that there are two types of edges aroused by the power-law index $a$ in the single-particle spectrum, i.e., an ergodic-to-multifractal edge for the long-range hopping case ($a<1$), and an ergodic-to-localized edge for the short-range hopping case ($a>1$). Meanwhile, the existence of these two types of edges is found to be robust against the non-Hermitian effect. By employing the Simon-Spence theory, we analyzed the absence of the localized states for $a<1$. For the short-range hopping case, with the Avila's global theory and the Sarnak method, we consider a specific example with $a=2$ to reveal the presence of the intermediate phase and to analytically locate the intermediate regime and the ergodic-to-multifractal edge, which are self-consistent with the numerically results.

8 pages, 8 figures

References in corpus (9)

• Topological phase transition in non-Hermitian quasicrystals
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Quantum Correlations in Two-Particle Anderson Localization
• Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Multifractality of Hamiltonians with power-law transfer terms
• Entanglement entropy and out-of-time-order correlator in the long-range Aubry-André-Harper model