Inverse Hamiltonian design by automatic differentiation

Abstract

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. Here, we develop a general framework that can automatically design a Hamiltonian with desired physical properties by using automatic differentiation. In the application to the quantum anomalous Hall effect, our framework can not only construct the Haldane model automatically but also generate Hamiltonians that exhibit 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 ~ 700 Am−2 under solar radiation. This framework would accelerate materials exploration by automatic construction of models and principles.