Quasiperiodic Systems Reveal Smooth Dynamics at the Mobility Edge.

Research into a one-dimensional quasiperiodic system, modelled by the generalised Aubry-André model, reveals a smooth transition between localised and extended states at a single-particle mobility edge. Entropic measurements and subsystem information capacity demonstrate a continuous change in dynamical signatures, confirming the mixed spectral nature of the system.

The behaviour of electrons within solid materials dictates many technological properties, and understanding how these particles move and interact remains a central challenge in condensed matter physics. Recent research has focused on quasiperiodic systems, materials that lack the translational symmetry of traditional crystals yet exhibit long-range order. These systems can host a ‘mobility edge’, a critical energy level separating localised and extended electron states, influencing how information propagates. Yuqi Qing, Yu-Qin Chen, and Shi-Xin Zhang, from the Institute of Physics, Chinese Academy of Sciences, and the Graduate School of China Academy of Engineering Physics, investigate this phenomenon in their article, ‘Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge’. Their work utilises the generalised Aubry-André model to explore how a mobility edge affects the dynamics of entanglement and information flow, offering insights into the behaviour of electrons in complex materials and establishing a benchmark for understanding similar dynamics in more intricate systems.

Recent research investigates the dynamics of quasiperiodic systems, utilising the generalised Aubry-André (GAA) model to explore information storage and propagation within systems possessing a single-particle mobility edge (SPME). The GAA model, a mathematical description of electron behaviour in a periodic potential with a quasiperiodic modulation, exhibits a smooth transition between localised and extended states, unlike systems displaying abrupt localisation changes. This characteristic makes it a valuable platform for studying information behaviour in mixed phases, where both types of states coexist. Researchers establish a non-interacting baseline to understand more complex, interacting systems, meticulously examining the interplay between system parameters, entanglement measures, and the emergence of these states.

The investigation employs both entanglement entropy (EE) and subsystem information capacity (SIC) as complementary tools to characterise the transition. Entanglement entropy quantifies the degree of quantum entanglement between different parts of a system, while subsystem information capacity measures the amount of information a subsystem can hold and transmit. Analysis reveals a consistent relationship between the system’s response to a sudden change, known as a quench, and the presence of both localised and extended states.

Results demonstrate that the SPME induces a smooth crossover in all observed dynamical signatures. Entanglement entropy achieves saturation with a persistent volume-law scaling within the mobility-edge phase. This indicates that entanglement grows proportionally to the size of the subsystem, a characteristic of extended systems, and demonstrates a continuous decrease in entropy density as the number of extended states diminishes. This signifies a gradual change in the system’s ability to store information as the proportion of localised states increases.

Complementing the entropy analysis, the subsystem information capacity profile demonstrates a clear interpolation between behaviours characteristic of extended and localised systems. It transitions from a linear ramp, indicative of extended states freely sharing information, to information trapping, a hallmark of localised states where information remains confined. This provides a direct visualisation of the mixed nature of the underlying spectrum, confirming the coexistence of localised and extended states within the mobility edge phase, offering a comprehensive picture of the system’s behaviour.

Researchers demonstrate the robustness of entanglement characteristics across varying initial states and measurement schemes within the one-dimensional quasiperiodic system governed by the GAA model. The findings consistently reveal a clear connection between changes in mutual information, a measure of information shared between subsystems, and the quantum phase transition occurring within the system, supporting the assertion that entanglement serves as a reliable indicator of the system’s evolving state. This meticulous analysis confirms that the observed behaviour remains consistent regardless of the specific initial conditions employed, utilising Néel, domain-wall, and random states to achieve consistent results.

The investigation confirms that the location of the entanglement probe does not influence the observed trends, employing both centre and edge coupling schemes for the reference qubit to strengthen the validity of the conclusions regarding the relationship between entanglement and the phase transition. Researchers establish a mixed symmetry-protected information content profile, indicating a more complex entanglement structure than simpler models, directly linking this complexity to the coexistence of localised and extended eigenstates within the system, a key characteristic of the single-particle mobility edge. This detailed analysis establishes a strong correlation between the saturation value of entanglement entropy and the number of localised states, reinforcing the idea that entanglement plays a crucial role in the emergence of many-body localisation.