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

TL;DR

This paper studies how entanglement and information capacity evolve in a one-dimensional quasiperiodic system with a single-particle mobility edge, revealing smooth crossovers and unique dynamical signatures of mixed localized and extended states.

Contribution

It provides the first detailed analysis of entanglement and information dynamics in a quasiperiodic system with a mobility edge, highlighting continuous crossover behaviors.

Findings

Volume-law entanglement scaling persists in the mobility-edge phase.

Subsystem information capacity interpolates between extended and localized behaviors.

Dynamical signatures serve as fingerprints of the 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-Andr\'e (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-Andr\'e 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.