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

Abstract

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.

Figures (8)

• Figure 1: Phase diagram of the GAA model, featuring three distinct dynamical regimes based on the potential strength $\lambda/|t|$ and deformation $a$. The model has completely extended (pink) and localized (green) phases, separated by an intermediate phase (yellow) where extended and localized states coexist due to the SPME.
• Figure 2: Energy spectrum of the GAA model for $a=0.3$ and $L=200$, with eigenstates colored by their IPR. The mobility edge $E_c$ (red lines), from Eq. (\ref{['eq:Ec']}), clearly separates extended states (low IPR, bright cyan) from localized states (high IPR, dark teal/black). This energy-dependent separation is a key feature of the SPME phase.
• Figure 3: Early-time EE growth velocity $v_S$ versus $\lambda/|t|$ for different $a$. The initial state is a Néel state with $L=200$. In contrast to the saturation entanglement, $v_S$ shows a smooth, monotonic decrease for both the AA ($a=0$) and GAA ($a>0$) models. This indicates that early-time dynamics are primarily sensitive to the potential strength rather than the detailed gap structure of the spectrum.
• Figure 4: Saturation EE $S_{\mathrm{sat}}$ versus $\lambda/|t|$ after a quench from the Néel state for $L = 200$. The AA model ($a = 0$, blue) has a sharp drop at the $\lambda = t$ transition. The GAA models ($a > 0$) show a smooth crossover, indicating partial delocalization caused by the SPME.
• Figure 5: Scaling exponent $\alpha$ of the saturation entropy ($S_{\mathrm{sat}} \propto L^\alpha$) versus $\lambda/|t|$. The exponent distinguishes area-law ($\alpha \approx 0$) from volume-law ($\alpha \approx 1$) scaling. Error bars indicate the standard error of the slope obtained from the linear regression fit. The inset shows a representative linear fit of $\ln S_{\mathrm{sat}}$ versus $\ln L$ for $a=0.3$ and $\lambda/|t|=1.0$. The persistent volume law for $a>0$ at intermediate $\lambda$ confirms the delocalizing effect of the SPME.