Inverse Hamiltonian design by automatic differentiation*

An ultimate goal of materials science is to deliver materials with desired properties at will. Solving the inverse problem to obtain an appropriate Hamiltonian directly from the desired properties has the potential to reach qualitatively new principles, but most research to date has been limited to quantitative determination of parameters within known models. In this study, we develop a general framework that can automatically design a Hamiltonian with desired physical properties by using automatic differentiation. By applying it to the quantum anomalous Hall effect, 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 anomalous Hall effect. In addition, the application to the photovoltaic effect gives an optimal Hamiltonian for electrons moving on a noncoplanar spin texture, which can generate ∼ 900 A/m² under solar radiation. Our framework is applicable to a wide range of quantum systems and physical properties, and will open up new directions to explore new models and principles in materials science.