Quasiperiodicity-Engineered Re-entrant Localization-Delocalization aspects in a Diamond Lattice

Abstract

We investigate localization in a quasiperiodically engineered diamond lattice with strand-dependent Aubry-André-Harper onsite modulations, highlighting the decisive roles of the modulation ratio $s$ and the averaged potential on the middle strand. The upper strand hosts the primary potential $λ$, the lower strand carries a weaker modulation $λ/s$, and the middle strand follows their average, generating a correlated quasiperiodic landscape across each plaquette. By tuning $λ$ for selected values of $s$, we probe spectral and eigenstate properties via the inverse participation ratio (IPR), normalized participation ratio (NPR), and fractal dimension $D_2$. We uncover a pronounced re-entrant localization behavior, where eigenstates repeatedly switch between extended and localized regimes, which persists only within a finite range of $s$ and crucially relies on the averaged potential construction. This unconventional sequence arises from the interplay of $s$, the correlated potential, and the intrinsic diamond geometry, producing a highly nontrivial interference landscape. Our results reveal localization physics beyond the standard Aubry-André paradigm, further supported by the evolution of extended states, system-size scaling of $\langle \mathrm{NPR} \rangle$ and $\langle D_2 \rangle$, and dynamical signatures from the time-dependent root-mean-square displacement, confirming the robustness of the re-entrant transitions.

Figures (24)

• Figure 1: Schematic diagram of a diamond lattice consisting of three strands denoted by I, II, and III, subjected to three different on-site potentials $\epsilon_1$, $\epsilon_2$, and $\epsilon_3$, where $\epsilon_2$ represents the average potential of the other two components.
• Figure 2: Eigenstates as a function of $\lambda$, colored by IPR in (a) and by NPR in (b). In (c), the averaged values $\langle IPR\rangle$ and $\langle NPR\rangle$ over the entire spectrum are plotted for $s=2$.
• Figure 3: The same graphical layout as in Fig. \ref{['fig:state1']}, but for $s=3$.
• Figure 4: Energy eigenvalues as a function of $\lambda$, colored by IPR in (a) and NPR in (b), respectively. The averaged values $\langle IPR\rangle$ and $\langle NPR\rangle$ for eigenvalues within the range $-0.5$ to $0.5$ are presented in (c). All calculations are performed for $s=2$.
• Figure 5: Similar characteristics as in Fig. \ref{['fig:band1']}, but for $s=3$.