Competing skin effect and quasiperiodic localization in the non-Hermitian Su-Schrieffer-Heeger chain: Reentrant delocalization, spectral topology destruction, and entanglement suppression

Abstract

We investigate the interplay between the non-Hermitian skin effect and Aubry-André-Harper (AAH) quasiperiodic disorder in a one-dimensional Su-Schrieffer-Heeger (SSH) chain with nonreciprocal hopping. By exact diagonalization, transfer-matrix analysis, and an analytical similarity-transformation argument, we map the full ( , $δ$) phase diagram, where A is the AAH modulation strength and the nonreciprocity parameter. We identify five distinct regimes: ( ) topological with extended bulk, (II) AAH-localized, (III) skin-localized, (IV) fully localized, and a previously unreported (V) competition regime exhibiting reentrant partial delocalization, in which intermediate quasiperiodic disorder disrupts the directional skin accumulation before ultimately Anderson-localizing all states. Using phase-averaged diagnostics and finite-size scaling, we confirm that the reentrant regime is robust, characterized by a non-monotonic inverse participation ratio that sharpens with increasing system size. We derive an analytical expression for the modified localization boundary $λ_{c}(δ)=2\sqrt{v_{eff}w}$ with $v_{vff}=\sqrt{v^{2}-δ^{2}}$, which agrees with numerical Lyapunov exponent calculations. We further show that quasiperiodic disorder progressively unwinds the complex spectral loops, destroying the point-gap topology at a critical strength distinct from the band-topological transition ; that the skin effect suppresses entanglement entropy to near-zero values while sufficiently strong AAH disorder partially restores it ; and that the SSH sublattice structure absent in the widely studied non-Hermitian AAH chain is essential for producing the five-phase landscape, as demonstrated by direct comparison with the non-dimerized limit.

Figures (11)

• Figure 1: Energy spectrum $\mathrm{Re}(E/w)$ versus $\lambda/w$ at $v/w = 0.5$, $N = 50$, colored by IPR. (a) $\delta = 0$; (b) $\delta/w = 0.3$; (c) $\delta/w = 0.6$. The localization transition at $\lambda_c/w \approx 2$ is progressively blurred by nonreciprocity.
• Figure 2: Superimposed probability density (blue) and near-zero-energy state (red) for four regimes. (a) Delocalized; (b) AAH localized; (c) skin effect; (d) competition. $v/w = 0.5$, $N = 50$.
• Figure 3: Phase diagram at $v/w = 0.5$, $N = 50$, $\phi = 0$. (a) Mean bulk IPR; (b) skin asymmetry; (c) fractal dimension $D_2$; (d) entanglement entropy $S(L/2)$. Dashed line: $\lambda_c/w = 2$.
• Figure 4: Complex energy spectra at $\delta/w = 0.5$, $N = 50$, for increasing $\lambda$. (a) $\lambda = 0$: elliptical loops; (b) $\lambda/w = 1$: partially scattered; (c) $\lambda/w = 2$: distorted; (d) $\lambda/w = 3.5$: real spectrum.
• Figure 5: Line-cut diagnostics at $\delta/w = 0$, $0.3$, $0.6$ (columns). Rows: mean IPR, biorthogonal polarization, entanglement entropy, Lyapunov exponent. $v/w = 0.5$, $N = 40$. Dotted line: $\lambda_c/w = 2$.