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arXiv 2602.19484cond-mat.str-el
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迈向热力学极限:神经算子用于Mott绝缘体的非平衡动力学

Toward the Thermodynamic Limit: Neural Operators for Non-equilibrium Dynamics of Mott Insulators

University of California, Irvine(加州大学尔湾分校);California Institute of Technology(加州理工学院);ETH Zürich(苏黎世联邦理工学院);NVIDIA Research(英伟达研究院)

Miles Waugh, Chuwei Wang, Radu Andrei, Nusair Islam, Taylor Lee Patti, Eugene Demler, Anima Anandkumar

AI总结:

本研究利用神经算子预测Mott绝缘体在强光驱动下的非平衡动力学,实现对大规模系统的零样本泛化,突破传统求解器的限制。

摘要:

Mott绝缘体在强光驱动下表现出复杂的光激发动力学,可能对超越Shockley-Queisser极限的载流子倍增具有潜在意义。探测这些非平衡过程需要访问热力学极限,即晶格点数变得任意大,但传统求解器因希伯特空间的指数增长而受限于小系统。傅里叶神经算子(FNOs),最初为求解偏微分方程而开发,能够自然适应不同分辨率的输入,并能捕捉非局部效应。在此,我们采用FNOs来学习从受扰动的基态动量分布到其脉冲后对应物的映射,覆盖多种相互作用强度和驱动参数。仅在小晶格上训练,该模型可泛化到更大系统,产生物理合理的动量分布,远超数值求解器的范围。具体而言,该模型可在数秒内预测1024x1024系统的动量分布,其行为与关键可观测量的理论行为一致,而直接数值模拟迄今为止仅能限制在边缘大小约为30的系统。这些结果展示了神经算子直接访问大规模非平衡动力学的潜力,为强相关材料的热力学极限提供了一条新途径。

英文摘要:

Mott insulators exhibit complex photoexcitation dynamics under intense optical driving, with potential implications for carrier multiplication beyond the Shockley-Queisser limit. Probing these nonequilibrium processes requires access to the thermodynamic limit, where the number of lattice sites becomes arbitrarily large, but conventional solvers are constrained to small systems due to the exponential growth of the Hilbert space. Fourier Neural Operators (FNOs), originally developed for solving partial differential equations, naturally accommodate inputs of varying resolution and are capable of capturing nonlocal effects. Here, we employ FNOs to learn the mapping from noise-perturbed ground-state momentum distributions to their post-pulse counterparts across a range of interaction strengths and driving parameters. Trained only on small lattices, the model generalizes zero-shot to much larger systems, producing physically reasonable momentum distributions well beyond the reach of numerical solvers. Specifically, the model can predict momentum distribution for a 1024x1024 system within a few seconds that matches the theoretical behavior of key observables, whereas direct numerical simulations have so far been restricted to edge sizes of ~30. These results demonstrate the potential of neural operators to directly access large-scale nonequilibrium dynamics, providing a new pathway toward the thermodynamic limit in strongly correlated materials.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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