Inverse Hamiltonian design by automatic differentiation

TL;DR

This paper introduces a framework using automatic differentiation for inverse Hamiltonian design, enabling the creation of new models with enhanced properties like larger anomalous Hall effects and photovoltaic responses.

Contribution

It presents a novel general method for inverse Hamiltonian design that can automatically generate Hamiltonians with desired properties, surpassing traditional parameter tuning.

Findings

Rediscovered the Haldane model for quantum anomalous Hall effect.

Generated a new Hamiltonian with six times larger AHE.

Designed an optimal Hamiltonian for photovoltaic effect under solar radiation.

Abstract

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.