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.