Interplay of Antiferromagnetism and Quasiperiodicity in a Hubbard Ring: Localization Insights

Abstract

We study localization in a quasiperiodic spinful antiferromagnetic Hubbard ring within a self-consistent Hartree-Fock framework, emphasizing the interplay of quasiperiodicity, staggered Zeeman-field-induced antiferromagnetic order, and electron correlations. Localization properties are characterized through inverse participation ratios, normalized participation ratios, and multifractality, and are consistently supported by a broad class of real-space mean-field observables, including double occupancy, density fluctuations, local entropy, spin-density-wave (SDW) order, and other related correlation measures. We uncover a pronounced nonmonotonic evolution of localization with interaction strength, featuring an intermediate regime marked by enhanced localization, strong spatial inhomogeneity, and magnetic ordering, followed by a re-entrant tendency toward delocalization at stronger interaction regime. Phase diagrams constructed from complementary localization and mean-field indicators reveal extended, localized, and critical regimes governed by the interplay of quasiperiodicity and interactions. Furthermore, real-time wave-packet dynamics of eigenstates provide direct evidence of ballistic spreading, confinement, and re-entrant transport, in agreement with the underlying spectral characteristics. These results establish a unified framework where diverse mean-field observables and dynamical probes consistently capture correlation-driven localization phenomena in quasiperiodic systems.

Figures (16)

• Figure 1: Schematic illustration of a spinful antiferromagnetic lattice with incommensurate hopping amplitudes, represented using distinct colors.
• Figure 2: Combined spin-resolved mean-field eigenvalue spectrum as a function of the Hubbard interaction $U$. For each value of $U$, all spin-up and spin-down eigenvalues obtained from the self-consistent Hartree mean-field decoupling are merged into a single set and plotted together. In the first column, we fix $h_z = 0.5$ and vary $\lambda$ from $0.5$ to $0.8$ in panels (a) and (c). In the second column, $\lambda$ is fixed at $0.5$, while $h_z$ is varied from $0.4$ to $0.8$ in panels (b) and (d), respectively.
• Figure 3: Spin-resolved energy splitting $\Delta E = E_{\uparrow}-E_{\downarrow}$ as a function of $U$, with the color scale representing $|\mathrm{IPR}{\uparrow}-\mathrm{IPR}{\downarrow}|$, shown for the same parameter-space orientation as in the preceding figure, highlighting the onset of interaction-driven spin-dependent localization.
• Figure 4: Figure shows the interaction-driven evolution of spin-resolved eigenstate profiles for $\lambda=0.5$, $h_z=0.4$ (top row) and $\lambda=0.8$, $h_z=0.8$ (bottom row). Panels (c) and (d) display $\Delta \mathrm{IPR}$, with the color scale capped at $0.20$ for enhanced visibility, consistent with the IPR-resolved spectral analysis.
• Figure 5: Variation of the average inverse participation ratio (AIPR) and average normalized participation ratio (ANPR) as functions of $U$ for four representative $\lambda$–$h_z$ parameter sets, corresponding to the parameter regimes shown in Fig. \ref{['fig:uegnval']}.