用自动微分法设计逆哈密顿量
Inverse Hamiltonian design by automatic differentiation
摘要：
材料科学的最终目标是任意地提供具有期望性质的材料。在理论研究中，标准的方法包括基于唯象学或第一性原理构造哈密顿量，计算物理可观量，并通过反馈改进哈密顿量。然而，也有一种方法，绕过这样一个繁琐的程序，即，获得一个适当的哈密顿量直接从所需的属性。解决反问题有可能达到定性不同的原则，但迄今为止，大多数研究已被限制在已知模型内的参数的定量测定。在这里，我们提出了一个通用的框架，使逆设计的哈密顿优化众多参数，使用自动微分。通过将其应用到量子反常霍尔效应（AHE）中，我们证明了我们的框架不仅可以重新发现Halfton模型，而且还可以自动生成一个新的哈密顿量，该哈密顿量表现出六倍大的AHE.此外，应用于光伏效应（PVE），给出了非共面自旋织构上电子运动的最佳哈密顿量，在太阳辐射下，该最佳哈密顿量可产生$\sim 900$ ~A/m $^2$.这一框架将通过建立超越人类直觉和经验规则的前所未有的模型和原则来加速材料探索。
英文摘要：
An ultimate goal of materials science is to deliver materials with desired properties at will. In the theoretical study, a standard approach consists of constructing a Hamiltonian based on phenomenology or first principles, calculating physical observables, and improving the Hamiltonian through feedback. However, there is also an approach that bypasses such a cumbersome procedure, namely, to obtain an appropriate Hamiltonian directly from the desired properties. Solving the inverse problem has the potential to reach qualitatively different principles, but most research to date has been limited to quantitative determination of parameters within known models. Here, we present a general framework that enables the inverse design of Hamiltonians by optimizing numerous parameters using automatic differentiation. By applying it to the quantum anomalous Hall effect (AHE), we show that our framework can not only rediscover the Haldane model but also automatically generate a new Hamiltonian that exhibits a six-times larger AHE. In addition, the application to the photovoltaic effect (PVE) gives an optimal Hamiltonian for electrons moving on a noncoplanar spin texture, which can generate $\sim 900$~A/m$^2$ under solar radiation. This framework would accelerate materials exploration by establishing unprecedented models and principles beyond human intuition and empirical rules.
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