Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge

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.

💡 Research Summary

The authors study quantum quench dynamics in the one‑dimensional generalized Aubry‑André (GAA) model, a non‑interacting spinless‑fermion system with a quasiperiodic on‑site potential that can host a single‑particle mobility edge (SPME). By varying the deformation parameter a and the potential strength λ, the model exhibits three regimes: a fully extended phase, a fully localized phase, and an intermediate phase where extended and localized eigenstates coexist because of the SPME. The paper first characterizes the static spectrum using the inverse participation ratio (IPR), confirming a clear energy threshold E_c that separates low‑IPR (extended) from high‑IPR (localized) states.

The dynamical protocol consists of a global quantum quench from a product Néel state (|1010…⟩) at half filling. Two complementary diagnostics are employed: (i) the bipartite entanglement entropy (EE) of the left half of the chain, and (ii) the subsystem information capacity (SIC), which quantifies how much quantum information initially localized on a single site can be recovered from a subsystem after time evolution.

Early‑time EE growth rates (v_S) decrease monotonically with λ for both the standard Aubry‑André model (a = 0) and the GAA model (a > 0). Importantly, v_S shows no plateaus or abrupt changes at the mobility‑edge energies, indicating that the initial spreading is governed by local kinetic constraints set by the quasiperiodic potential rather than the global spectral structure.

In contrast, the long‑time saturation EE (S_sat) displays markedly different behavior. For the AA model, S_sat drops sharply at the known transition λ = t, reflecting a switch from volume‑law (thermal‑like) to area‑law (localized) scaling. In the GAA model, S_sat varies smoothly with λ, producing a crossover rather than a sharp transition. Finite‑size scaling of S_sat ∝ L^α reveals that α≈1 (volume law) persists throughout the intermediate SPME regime (e.g., λ/|t| = 1.0–1.3), while α≈0 (area law) is recovered only for large λ. Moreover, S_sat correlates one‑to‑one with the fraction of extended states n_e = N_e/L, confirming that the capacity to generate extensive entanglement is directly proportional to the number of available extended single‑particle modes.

To resolve spatial information flow, the authors compute SIC. They entangle a reference qubit R with a single central site E, evolve the system, and evaluate the mutual information I(A:R) between R and a contiguous subsystem A of size |A| centered on E. In a fully extended system, I(A:R) grows linearly with |A| (ballistic information transport). In a fully localized system, I(A:R) exhibits a step‑function: a rapid rise for the smallest subsystems (information trapped near E) followed by a flat plateau. In the GAA model’s SPME phase, the SIC profile is hybrid: an initial jump (reflecting trapping by localized states) is followed by a slower, approximately linear increase (due to ballistic spreading through the remaining extended states). The magnitude of the initial jump correlates strongly with the fraction of localized states n_l = N_l/L, providing a quantitative link between spectral composition and information trapping.

Overall, the study demonstrates that a single‑particle mobility edge reshapes both entanglement generation and information propagation: EE retains a volume law but with a continuously tunable prefactor set by the extended‑state fraction, while SIC offers a spatially resolved fingerprint of the coexistence of localized and extended dynamics. These results constitute a clear non‑interacting benchmark for future investigations of interacting systems where many‑body mobility edges or many‑body localization–thermalization transitions may occur. The work also suggests concrete experimental protocols for ultracold‑atom or photonic‑lattice realizations of the GAA model, where both EE and SIC (or related mutual‑information measurements) could be accessed to probe mobility‑edge physics.