We study interaction-induced localization in a spinful quasiperiodic Hubbard ring with quasiperiodically modulated hopping and a staggered spin-dependent Zeeman field using a self-consistent Hartree-Fock approach. We characterize localization through the inverse participation ratio, normalized participation ratio, and multifractal analysis, and further examine its signatures in self-consistent real-space observables, including double occupancy, density fluctuations, local entropy, spin-density-wave order, and related correlation measures. As the Hubbard interaction is increased, we find a nonmonotonic evolution of the eigenstates: an initially extended regime gives way to an intermediate localized phase, followed by reentrant delocalization at stronger interactions. The width of this intermediate regime grows systematically with both the quasiperiodic hopping amplitude and the staggered Zeeman-field strength, indicating a cooperative enhancement of localization by these two ingredients. In the localized regime, the self-consistent interaction produces pronounced spin dependence in both the spectra and localization properties, resulting in distinct responses of the spin-up and spin-down sectors. The interaction-driven crossover is consistently captured by the real-space observables and further corroborated by real-time wave-packet dynamics, which reveal successive ballistic, confined, and reentrant-transport regimes consistent with the underlying eigenstate character. These results provide a unified framework for understanding the interplay of quasiperiodicity, electronic interactions, and spin-dependent fields in controlling localization, criticality, and quantum transport in correlated quasiperiodic systems.
We study interaction-induced localization in a spinful quasiperiodic Hubbard ring with quasiperiodically modulated hopping and a staggered spin-dependent Zeeman field using a self-consistent Hartree-Fock approach. We characterize localization through the inverse participation ratio, normalized participation ratio, and multifractal analysis, and further examine its signatures in self-consistent real-space observables, including double occupancy, density fluctuations, local entropy, spin-density-wave order, and related correlation measures. As the Hubbard interaction is increased, we find a nonmonotonic evolution of the eigenstates: an initially extended regime gives way to an intermediate localized phase, followed by reentrant delocalization at stronger interactions. The width of this intermediate regime grows systematically with both the quasiperiodic hopping amplitude and the staggered Zeeman-field strength, indicating a cooperative enhancement of localization by these two ingredients. In the localized regime, the self-consistent interaction produces pronounced spin dependence in both the spectra and localization properties, resulting in distinct responses of the spin-up and spin-down sectors. The interaction-driven crossover is consistently captured by the real-space observables and further corroborated by real-time wave-packet dynamics, which reveal successive ballistic, confined, and reentrant-transport regimes consistent with the underlying eigenstate character. These results provide a unified framework for understanding the interplay of quasiperiodicity, electronic interactions, and spin-dependent fields in controlling localization, criticality, and quantum transport in correlated quasiperiodic systems.
We investigate persistent charge and spin currents in a one-dimensional quantum ring threaded by an Aharonov-Bohm (AB) flux, considering generalized Aubry-André-Harper (AAH) modulation with staggered onsite energies and antiferromagnetic (AFM) ordering in both the noninteracting and interacting regimes, with the latter treated using a self-consistent Hartree-Fock mean field theory (MFT). At half filling, two distinct current-enhancement peaks emerge as the modulation strength increases, with quasiperiodic hopping modulation playing a crucial role in establishing the two-peak structure within a restricted parameter regime. Spin-resolved bond-current profiles reveal a switch in the dominant spin contribution between the two peaks, while the inverse participation ratio (IPR) and flux-dependent spin-resolved ground-state energies provide complementary insights into the spatial characteristics of the eigenstates and their spin-dependent flux sensitivity. At quarter filling, the spin current exhibits a single enhancement peak, in contrast to the two-peak response observed at half filling. The Hubbard interaction affects the two half-filled peaks differently: it suppresses the primary peak, whereas the secondary peak exhibits a nonmonotonic, re-entrant response, with the current recovering at finite interaction strength. The interacting results are further characterized through the Drude weight, and comparisons with exact diagonalization (ED) and density-matrix renormalization group (DMRG) calculations for a finite half-filled system support the reliability of the MFT description. Our findings elucidate how quasiperiodic modulation, AFM order, band filling, and electronic correlations collectively govern the magnitude and spin-resolved character of persistent currents, giving rise to multiple enhancement regimes and interaction-induced re-entrant behavior.
A reentrant localization transition was predicted recently in a one-dimensional quasiperiodic lattice with dimerized hopping between the nearest-neighbor sites [Roy et al., Phys. Rev. Lett. 126, 106803 (2021)]. It was shown that the interplay between the hopping dimerization and a staggered quasiperiodic disorder manifests two localization transitions through two intermediate phases, resulting in four critical points as a function of the quasiperiodic potential. In this paper, we study the critical nature of the states across the localization transitions by computing the mass exponents and the corresponding fractal dimensions of the states through a multifractal analysis. Moreover, we analyze the phenomenon of this reentrant localization transition by examining the spectral properties of the eigenstates. By performing a systematic finite-size scaling analysis for a fixed value of the hopping dimerization, we obtain accurate critical disorder strengths for different transitions and the associated critical exponents. Further, we complement the critical nature of the energy spectrum by computing the Hausdorff dimensions.
Abstract Correlation-driven metal–insulator transitions and temperature-driven coherence–incoherence crossovers strongly influence the dynamical responses of correlated electron systems. Motivated by recent experimental probes of spin and charge excitations, we investigate the real-frequency local spin and charge dynamical susceptibilities of the one-band Hubbard model within dynamical mean-field theory (DMFT), employing numerical renormalization group (NRG) impurity solvers. We analyze both the interaction-driven transition at half filling and the temperature evolution in the doped regime proximate to the Mott insulator. To characterize low-energy relaxation processes within the local DMFT framework, we examine normalized dissipative spectra constructed from the imaginary parts of the local susceptibilities. From these spectra we extract characteristic fluctuation scales and track their evolution with interaction strength, temperature, and band filling. At half filling, the spin and charge channels exhibit qualitatively distinct low-frequency structures governed by symmetry and correlation effects. In the doped Mott regime, we find that spin and charge fluctuations reorganize on parametrically different temperature scales, signaling a separation of local coherence scales within a purely local theory. We emphasize that our analysis pertains to on-site dynamical relaxation within DMFT rather than hydrodynamic transport. Nevertheless, the distinct temperature evolution of spin and charge fluctuation scales is qualitatively consistent with multistage crossover behavior observed in transport quantities. These results highlight how local two-particle dynamics reorganize across interaction- and temperature-driven crossovers near the Mott transition.
Proximity effects, in which one subsystem imprints its properties onto another, offer a route to controlling quantum matter. For localization, this raises the question of whether an extended system can be localized by its neighbor, and then delocalized again, in the regime of weak quasiperiodic disorder. Here, we demonstrate this behavior in a coupled Aubry--André ladder, where a staggered detuning applied to only one leg localizes the neighboring, undetuned leg through inter-leg hybridization, even before the detuned leg itself localizes. Upon further increasing the detuning, the undetuned leg undergoes re-entrant delocalization, while the detuned leg remains localized. Finite-size scaling supports the persistence of these regimes in the thermodynamic limit. On an IBM Quantum processor, we experimentally observe their dynamical signatures: strongly suppressed wave-packet spreading in the proximity-localized regime and its recovery upon re-entrant delocalization. Our results establish leg-selective detuning as a reversible control knob for localization and transport in coupled quantum systems.
We investigate circular current in both ordered and disordered Hubbard quantum rings threaded by magnetic flux, employing exact diagonalization and the Hartree-Fock mean-field approach within the tight-binding framework. The influence of on-site and extended Hubbard interactions, disorder, and electron filling on the persistent current is systematically analyzed. To construct the full many-body Hamiltonian, we introduce a linear table formalism, which, to our knowledge, has been rarely used in this context. In ordered rings, the current decreases monotonically with increasing on-site repulsion, while the impact of the extended interaction depends strongly on the filling factor. At low filling, stronger extended interaction suppresses the current, whereas near half-filling, it enhances the current up to a critical ratio, half of the on-site strength, before reducing it. Disorder significantly modifies these behaviors, notably enhancing the current at less than quarter-filling with increasing extended interaction. The localization properties of eigenstates, examined via the inverse participation ratio, further support the crucial roles of filling and the interplay between on-site and extended interactions in governing persistent current.
Localization-delocalization transition and PT-symmetry breaking via second-neighbor coupling in a Heisenberg spin chain
The exploration of non-Hermitian quantum systems, particularly those governed by parity-time ([Formula: see text])-symmetry, has revealed a rich landscape of unconventional phase transitions and localization phenomena. Spin chains with quasiperiodic potentials and competing Heisenberg interactions provide a versatile framework for probing these effects. In this study, we investigate the dynamical and spectral signatures of [Formula: see text]-symmetry breaking and localization-delocalization transitions in spin chains subjected to a non-Hermitian Aubry-André potential and tunable Heisenberg couplings across nearest ([Formula: see text]) and next-nearest neighbors ([Formula: see text]). Our analysis reveals that increasing [Formula: see text] monotonically shifts the critical point [Formula: see text], while [Formula: see text] induces a non-linear response, generating a distinct minimum in [Formula: see text]. Notably, [Formula: see text] leads to the emergence of partially imaginary eigenvalues beyond [Formula: see text], decoupling the onset of [Formula: see text]-symmetry breaking from the localization transition. Using inverse and normalized participation ratios, we identify three distinct phases: extended, localized, and an intermediate hybrid regime characterized by a mobility edge. To capture the dynamical fingerprints of these phases, we employ time-dependent density distribution, long-time survival probability [Formula: see text], analysis. Extended phases exhibit ballistic spreading and algebraic decay, while localized regimes show spatial confinement and exponential decay. These observables serve as robust indicators of non-Hermitian phase transitions, offering insights beyond static spectral measures. Overall, our findings underscore the critical role of dynamical metrics in characterizing phase structure in non-Hermitian spin systems. As interest in non-equilibrium quantum dynamics continues to grow, such models provide a compelling platform for understanding the interplay between [Formula: see text]-symmetry, localization, and quantum coherence in complex many-body systems.