Zhang, J., Rajabpour, M. A., Heyl, M., & Khasseh, R. (2024). Subsystem Evolution Speed as Indicator of Relaxation. arXiv preprint arXiv:2410.17798.
This paper introduces a novel method for assessing relaxation in isolated quantum many-body systems by analyzing the evolution speed of subsystems, aiming to provide a tool that bypasses the limitations of traditional approaches relying on local operators or prior knowledge of the steady state.
The researchers define the evolution speed of a subsystem as the rate of change of its reduced density matrix over time, utilizing the trace distance as a measure of distance between quantum states. They then investigate the behavior of this metric in various quantum models, including the chaotic Ising chain, XXZ chains with and without many-body localization (MBL), and the transverse field Ising chain, comparing their findings with established relaxation indicators.
The study reveals that the subsystem evolution speed decreases as the overall system size increases in systems approaching relaxation, particularly for subsystems smaller than half the total system size. This trend is consistent with the behavior of the subsystem trace distance to the steady state and aligns with the predictions of the eigenstate thermalization hypothesis (ETH). The researchers demonstrate the robustness of their method across different initial states and models, including those exhibiting thermalization, integrability, and MBL.
The subsystem evolution speed offers a reliable and accurate indicator of relaxation in quantum many-body systems, independent of specific local operators or prior knowledge of the steady state. This approach provides a valuable tool for investigating relaxation dynamics in complex quantum systems, potentially offering insights into the transition from integrable to ergodic dynamics.
This research introduces a novel perspective on analyzing relaxation in quantum systems, potentially impacting the study of quantum dynamics, thermalization, and the characteristics of many-body localized phases. The proposed method's simplicity and reliance solely on the system's state make it a powerful tool for exploring a wide range of quantum phenomena.
While the study validates the method across several models, further investigation into more complex systems, such as those with higher dimensions, long-range interactions, and diverse symmetries, is necessary to confirm its general applicability. Additionally, a deeper theoretical understanding of the relationship between subsystem evolution speed and fundamental dynamical processes in quantum systems is crucial for fully leveraging its potential.
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by Jiaju Zhang,... at arxiv.org 10-24-2024
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