Machine Learning Hamiltonians with Polarizations for Heterogeneous Systems
Abstract
Machine learning Hamiltonians use local atomic structures to determine local Hamiltonian matrix elements without carrying out self-consistent calculations. They have been used to study large systems and to carry out high-throughput screening for their electronic and optical properties. The prediction of the Hamiltonian is essentially the prediction of the electron electrostatic potential energy; however, for heterogeneous systems, this potential energy is often determined by faraway features, such as interface or surface dipoles, or even an applied voltage in a nanodevice. Thus, it cannot be determined by local atomic structures alone. In this sense, one needs to solve the electron electrostatic potential energy self-consistently using intrinsic atomic dipoles, the applied external potential energy, and polarizabilities. Fortunately, the intrinsic dipoles and polarizabilities are local properties, whereas the applied potential energy is a prescribed input. In this work, we propose DeepH-Polar, a physically informed machine learning Hamiltonian model that explicitly predicts intrinsic atomic dipoles and polarizability tensors and uses them to solve the electron electrostatic potential energy self-consistently. Benchmarks on polar GaN systems and crystalline-Si/amorphous-SiO2 interfaces demonstrate improved Hamiltonian accuracy and reproduction of thickness-dependent electrostatic variations, as well as spatially nonuniform field-induced screening that models without polarization fail to capture. Our model also allows us to study nanoscale electronic devices. By iteratively solving the Hamiltonian eigenproblem and self-consistently updating free-carrier occupations and the electrostatic potential, we simulate an 8,194-atom gated semiconductor device.
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BibTeX
@misc{zhou2026machine,
title = {{Machine Learning Hamiltonians with Polarizations for Heterogeneous Systems}},
author = {Jia-Yu Zhou and Wentao Zhang and Mouyi Weng and Zhao-Yi Yan and Lin-Wang Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36839},
eprint = {2610.36839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36839},
}
RIS
TY - UNPB
TI - Machine Learning Hamiltonians with Polarizations for Heterogeneous Systems
AU - Jia-Yu Zhou
AU - Wentao Zhang
AU - Mouyi Weng
AU - Zhao-Yi Yan
AU - Lin-Wang Wang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36839
UR - https://arxiv.org/abs/2610.36839
AB - Machine learning Hamiltonians use local atomic structures to determine local Hamiltonian matrix elements without carrying out self-consistent calculations. They have been used to study large systems and to carry out high-throughput screening for their electronic and optical properties. The prediction of the Hamiltonian is essentially the prediction of the electron electrostatic potential energy; however, for heterogeneous systems, this potential energy is often determined by faraway features, such as interface or surface dipoles, or even an applied voltage in a nanodevice. Thus, it cannot be determined by local atomic structures alone. In this sense, one needs to solve the electron electrostatic potential energy self-consistently using intrinsic atomic dipoles, the applied external potential energy, and polarizabilities. Fortunately, the intrinsic dipoles and polarizabilities are local properties, whereas the applied potential energy is a prescribed input. In this work, we propose DeepH-Polar, a physically informed machine learning Hamiltonian model that explicitly predicts intrinsic atomic dipoles and polarizability tensors and uses them to solve the electron electrostatic potential energy self-consistently. Benchmarks on polar GaN systems and crystalline-Si/amorphous-SiO_2 interfaces demonstrate improved Hamiltonian accuracy and reproduction of thickness-dependent electrostatic variations, as well as spatially nonuniform field-induced screening that models without polarization fail to capture. Our model also allows us to study nanoscale electronic devices. By iteratively solving the Hamiltonian eigenproblem and self-consistently updating free-carrier occupations and the electrostatic potential, we simulate an 8,194-atom gated semiconductor device.
ER -