We investigate the quantum dynamics of a one-dimensional quasiperiodic system featuring a single-particle mobility edge (SPME), described by the generalized Aubry-André (GAA) model. This model offers a unique platform to study the consequences of coexisting localized and extended eigenstates, which contrasts sharply with the abrupt localization transition in the standard Aubry-André model. We analyze the system's response to a quantum quench through two complementary probes: entanglement entropy (EE) and subsystem information capacity (SIC). We find that the SPME induces a smooth crossover in all dynamical signatures. The EE saturation value exhibits a persistent volume-law scaling in the mobility-edge phase, with an entropy density that continuously decreases as the number of available extended states decreases. Complementing this, the SIC profile interpolates between the linear ramp characteristic of extended systems and the information trapping behavior of localized ones, directly visualizing the mixed nature of the underlying spectrum. Our results establish unambiguous dynamical fingerprints of a mobility edge, providing a crucial non-interacting benchmark for understanding information and entanglement dynamics in more complex systems with mixed phases.
We investigate the quantum dynamics of a one-dimensional quasiperiodic system featuring a single-particle mobility edge (SPME), described by the generalized Aubry-André (GAA) model. This model offers a unique platform to study the consequences of coexisting localized and extended eigenstates, which contrasts sharply with the abrupt localization transition in the standard Aubry-André model. We analyze the system's response to a quantum quench through two complementary probes: entanglement entropy (EE) and subsystem information capacity (SIC). We find that the SPME induces a smooth crossover in all dynamical signatures. The EE saturation value exhibits a persistent volume-law scaling in the mobility-edge phase, with an entropy density that continuously decreases as the number of available extended states decreases. Complementing this, the SIC profile interpolates between the linear ramp characteristic of extended systems and the information trapping behavior of localized ones, directly visualizing the mixed nature of the underlying spectrum. Our results establish unambiguous dynamical fingerprints of a mobility edge, providing a crucial non-interacting benchmark for understanding information and entanglement dynamics in more complex systems with mixed phases.
We systematically investigate the entanglement and information dynamics of quasiperiodic systems across their extended, critical, and localized phases, aiming to identify dynamical signatures that can reveal the multifractal spatial structure of critical states and distinguish critical phases from the extended and localized regimes. Focusing on the generalized Aubry-André-Harper model, we complement the half-chain entanglement entropy with the spatially resolved subsystem information capacity (SIC) and demonstrate that critical states exhibit pronounced spatial heterogeneity absent in the extended and localized phases. In the steady state, the SIC reveals a stepwise ramp as a function of subsystem size, reflecting an underlying fragmentation of the chain into weakly connected subregions. Dynamically, information initially localized within such a subregion can undergo coherent long-lived oscillations, dubbed subregion echoes, whose period scales with the subregion length, in quantitative agreement with a quasiparticle picture of confined quasiparticle reflections. We trace this internal fragmentation to the incommensurately distributed zeros (IDZs) in the off-diagonal hopping terms of the Hamiltonian. To establish the generality of the SIC as a diagnostic tool, we further apply it to a mobility-edge phase with coexisting extended and localized states and to a critical phase that does not originate from IDZ fragmentation, and show that the SIC can cleanly distinguish these scenarios through their distinct steady-state profiles, initial-site sensitivities, and the presence or absence of subregion echoes. Our results demonstrate that the SIC serves as a powerful real-space probe for diagnosing critical phases and uncovering the bottlenecked connectivity that underlies the multifractal structure of critical states.
We develop a theoretical scheme to perform a readout of the properties of a quasiperiodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a one-dimensional quasiperiodic system with a potential given by the Andr\'e-Aubry-Harper (AAH) model and its generalized versions (GAAH model) is sensitive to the nature of the single-particle eigenstates (SPEs). More specifically, we can use the non-Markovianity of the qubit dynamics as quantified by the backflow of information to clearly distinguish the localized, delocalized, and mixed regimes with a mobility edge of the AAH and GAAH models and evidence the transition between them. By attaching two qubits at distinct sites of the system, we demonstrate that the transport property of the quasiperiodic system is encoded in the scaling of the threshold time to develop correlations between the qubits with the distance between the qubits. This scaling can also be used to distinguish and infer different regimes of transport such as ballistic, diffusive, and no transport engendered by SPEs that are delocalized, critical, and localized respectively. In addition, the localization length of the SPEs can also be gleaned from the exponential decay of correlations at long times as a function of distance between qubits. When there is a mobility edge allowing the coexistence of different kinds of SPEs in the spectrum, such as the coexistence of localized and delocalized states in the GAAH models, we find that the transport behavior and the scaling of the threshold time with qubit separation are governed by the fastest spreading states.
A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, in a quasiperiodic system, the localization transition can occur at a finite detuning strength and SPMEs become possible. In this Letter, we find experimental evidence for the existence of such a SPME in a one-dimensional quasiperiodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime.
One-dimensional quasiperiodic systems with power-law hopping, 1/r^{a}, differ from both the standard Aubry-André (AA) model and from power-law systems with uncorrelated disorder. Whereas in the AA model all single-particle states undergo a transition from ergodic to localized at a critical quasidisorder strength, short-range power-law hops with a>1 can result in mobility edges. We find that there is no localization for long-range hops with a≤1, in contrast to the case of uncorrelated disorder. Systems with long-range hops rather present ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but nonergodic) states. Both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.
A generalization of the Aubry-Andr\'e model, the noninteracting Ganeshan-Pixley-Das Sarma model (GPD) introduced by Ganeshan et al. [Phys. Rev. Lett. 114, 146601 (2015)], is known analytically to possess a mobility edge, allowing both extended and localized eigenstates to coexist. This mobility edge has been hypothesized to survive in closed many-body interacting systems, giving rise to a new nonergodic metallic phase. In this work, coupling the interacting GPD model to a thermal bath, we provide direct numerical evidence for multiple qualitative behaviors in the parameter space of disorder strength and energy level. In particular, we look at the bath-induced saturation of entanglement entropy to classify three behaviors: thermalized, nonergodic extended, and localized. We also extract the localization length in the localized phase using the long-time dynamics of the entanglement entropy and the spin imbalance. Our work demonstrates the rich localization landscape of generalized Aubry-Andr\'e models containing mobility edges in contrast to the simple Aubry-Andr\'e model with no mobility edge.
We investigate many-body localization in the presence of a single-particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single-particle mobility edge in the noninteracting system leads to a many-body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the nonthermal to thermal transition. Consequently, there exists an extended nonergodic phase for an intermediate energy window where the many-body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many-body localization transition despite the existence of a single-particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.