Inverse Hamiltonian design by automatic differentiation

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.

References in corpus (10)

• Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics
• Gradient-based optimal control of open quantum systems using quantum trajectories and automatic differentiation
• Chiral Soliton Lattice Formation in Monoaxial Helimagnet Yb(Ni${}_{1-x}$Cu${}_x$)${}_3$Al${}_9$
• DQC: a Python program package for Differentiable Quantum Chemistry
• Automatic Differentiation for the Direct Minimization Approach to the Hartree-Fock Method
• Quadratic Optical Responses in a Chiral Magnet
• Automatic Differentiable Numerical Renormalization Group
• Learning Effective Spin Hamiltonian of Quantum Magnet
• dPV: An End-to-End Differentiable Solar-Cell Simulator
• Engineering Topological Phases Guided by Statistical and Machine Learning Methods

Cited by in corpus (5)

• Exploring topological spin order by inverse Hamiltonian design: A new stabilization mechanism for square skyrmion crystals
• Inverse Hamiltonian design of highly-entangled quantum systems
• Non-Hermitian Parent Hamiltonian from Generalized Quantum Covariance Matrix
• Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals
• Inverse magneto-conductance design by automatic differentiation