[论文解读] Many-body mobility edges in one dimension revealed by efficient and interpretable feature-based learning with Kolmogorov-Arnold Networks

Siqi Dai, Tian-Cheng Yi+2 more|arXiv (Cornell University)|Mar 23, 2026

Quantum many-body systems被引用 0

一句话总结

论文使用四特征、基于物理信息的Kolmogorov–Arnold Network (KAN) 来识别遍历态与MBL态，并在1D有序费米子系统中揭示能量分辨的多体可移动边界，准确度>99.9%。

ABSTRACT

We study the many-body localization (MBL) transition in interacting fermionic systems on disordered one-dimensional lattices using a physics-informed machine-learning framework. Instead of feeding full many-body wave functions into the model, we construct a compact feature representation based on four physically motivated observables: the inverse participation ratio, the Shannon entropy, the many-body hybridization parameter, and the mean level-spacing ratio. These quantities capture complementary aspects of localization, entanglement, and spectral correlations, and are used to train a Kolmogorov--Arnold Network (KAN) classifier on eigenstates deep in the weak and strong disorder regimes. The resulting KAN achieves a validation accuracy exceeding $99.9\%$, comparable to that of convolutional neural networks trained directly on high-dimensional wave-function data, while requiring substantially reduced input dimensionality and significantly shorter training time. Applying the trained classifier across the full energy spectrum yields energy-resolved phase diagrams that reveal a clear many-body mobility edge and provide a consistent estimate of the critical disorder strength. The approach is inherently extensible: additional physically relevant observables can be incorporated into the feature space in a systematic manner without altering the overall architecture. Our results demonstrate that feature-based learning with KAN provides an efficient, scalable, and interpretable methodology for identifying many-body localization transitions, offering a practical alternative to raw-data-based neural network approaches.

研究动机与目标

• 在一维有序费米子系统中激发并识别遍历到多体局域化（MBL）转变。
• 使用紧凑、可解释的特征集开发物理信息化的机器学习分类器。
• 将基于特征的学习（KAN）与在完整波函数数据上训练的CNN进行比较，以评估效率和可解释性。
• 生成能量分辨的相图，显示跨光谱的多体移动边界。

提出的方法

• 从每个本征态的四个可观测量构建紧凑特征向量：ln(IPR)、Shannon熵S、多体混合参数g，以及平均能级间距比<r>。
• 在遍历态和MBL区深处的特征上训练Kolmogorov–Arnold Network (KAN) 分类器，并将其应用于整个光谱以绘制相图。
• 使用二元分类损失(BCEWithLogitsLoss)并采用Adam优化，输出sigmoid以获得概率相预测。
• 将KAN与在完整波函数概率密度上训练的CNN进行比较，以基准性能与可解释性。
• 采用能量分箱并对无序实现进行求平均，构建能量分辨的相图并识别多体移动边界。

Figure 2 : Architecture of the KAN model with shape $[4,5,1]$ . Learnable activation functions $\phi_{l,q,p}$ , parameterized as B-spline curves, are associated with the edges rather than the nodes. The color intensity of each connection indicates its relative importance. Edges with importance score

实验结果

研究问题

• RQ1 低维、物理信息化的特征集结合KAN是否能可靠地将遍历态与MBL本征态区分开？
• RQ2 KAN给出的能量分辨相图与基于CNN的方法及传统诊断相比如何？
• RQ3 在推动分类的各观测量中起作用的角色以及边缘贡献在何处？
• RQ4 基于特征的方法是否能给出清晰的多体移动边界以及跨光谱的一致临界无序强度？

主要发现

• KAN在测试数据上实现了超过99.9%的验证准确度，与在完整波函数数据上训练的CNN相当。
• KAN给出的能量分辨相图再现了全局相结构和随着无序强度弯曲的多体移动边界。
• 相图在约Wc ~ 2.8处显示出跨越，与前人工作一致。
• 边缘重要性分析显示ln(IPR)和S在阈值以上对边界贡献更大，表明它们在判定函数中的作用更强。
• 使用所有四个特征比单一观测量更鲁棒，边界更清晰。
• KAN的训练速度明显快于CNN，同时保持可比的预测性能，并提供对特征贡献的显式可解释性。

Figure 3 : Illustration of the B-spline construction for the target function $\phi_{0,5,1}$ (solid black curve), which is computed via Eq. ( 7 ). The six colored dashed curves correspond to the six B-spline basis functions whose weighted sum forms $\phi_{0,5,1}$ . The horizontal axis represents the