通过动态模式分解预测量子多体系统中的长时间动力学
Forecasting long-time dynamics in quantum many-body systems by dynamic mode decomposition
AI总结：
本文利用动态模式分解（DMD）基于短时数据预测量子多体系统（如临界横向场伊辛模型）的长时间动力学，证明其能准确预测近一个数量级更长的时间，且对少量噪声具有鲁棒性。
摘要：
当长程量子纠缠在强关联系统中发挥关键作用（如量子临界性主导的情形）时，量子动力学的可靠数值计算是一个基本挑战。本文应用一种利用物理量的可靠短时数据来准确预测强纠缠系统长时间行为的方法。我们直接采用流体动力学中常用的简单动态模式分解（DMD）。尽管该方法简单，但DMD在量子多体系统（如临界点处的横向场伊辛模型）中的有效性和适用性得到了证明，即使在长时间演化表现出复杂特征（如体积律纠缠熵以及由长程量子纠缠导致的特征性关联幂律衰减，这与流体动力学不同）时也是如此。本方法虽然简单，但能够在比短时训练数据长约近一个数量级的时间内实现惊人准确的预测。我们还研究了噪声对预测精度的影响，因为这在处理实验数据时尤为重要。我们发现，百分之几的噪声不会对预测精度造成破坏性影响。
英文摘要：
Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a method that utilizes reliable short-time data of physical quantities to accurately forecast long-time behavior of the strongly entangled systems. We straightforwardly employ the simple dynamic mode decomposition (DMD), which is commonly used in fluid dynamics. Despite the simplicity of the method, the effectiveness and applicability of the DMD in quantum many-body systems such as the Ising model in the transverse field at the critical point are demonstrated, even when the time evolution at long time exhibits complicated features such as a volume-law entanglement entropy and consequential power-law decays of correlations characteristic of systems with long-ranged quantum entanglements unlike fluid dynamics. The present method, though simple, enables accurate forecasts amazingly at time as long as nearly an order of magnitude longer than that of the short-time training data. Effects of noise on the accuracy of the forecast are also investigated, because they are important especially when dealing with the experimental data. We find that a few percentages of noise do not affect the prediction accuracy destructively.
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