Physical structure as an organizing principle for universal Hamiltonian learning
Abstract
Density functional theory (DFT) gives the electronic structure of materials, but its cost limits large-supercell calculations and materials screening. Machine-learned Hamiltonians bypass the self-consistent cycle but are usually system-specific; universal ones could cover new compositions and disordered solids. Such models must generalize across chemistry and keep downstream properties physical, while staying inexpensive for large cells. Here we introduce UniTB, a universal E(3) equivariant Hamiltonian representation framework that integrates physical priors rooted in density-functional tight-binding theory with deep learning. UniTB's network, which corrects a prior Hamiltonian, generalizes across chemistry through a mixture of experts routed by that prior and a charge-equilibration head as in self-consistent-charge tight binding. A projection bounds band shifts from the prior, suppressing spurious states and keeping downstream properties physical. We provide the fastest SO(2) tensor-product GPU kernels for the network. The variant UniTB-Flash assembles its prior from two-center tables at O(N) cost for N atoms, against O(Nlog N) on a grid. Trained on 29,242 crystals, UniTB reaches a 0.48 meV matrix-element error on nonmagnetic test crystals spanning 68 elements. Without amorphous training data, both models agree with DFT optics and conductivity of amorphous Ge-Sb-Te. UniTB-Flash ranks candidates with no significant difference from UniTB, whose property values are more accurate; together they screen 16,195 crystals for five application domains of industrial relevance.
Related
- The cubic discriminant as an organizing principle for Duffing dynamics
- Floquet-Universal Hamiltonian Simulation
- Constraints for Physical Gauge Groups Coming from the Causal Action Principle
- Joint Mitigation of Algorithmic and Physical Errors in Noisy Hamiltonian Simulation
- A Single Physical Principle Determines Quantum Relative Entropy
BibTeX
@misc{liu2026physical,
title = {{Physical structure as an organizing principle for universal Hamiltonian learning}},
author = {Mingkang Liu and Zhanghao Zhouyin and Guanghui Wang and Daye Zheng and Lei Shen and Qiangqiang Gu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36135},
eprint = {2610.36135},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36135},
}
RIS
TY - UNPB
TI - Physical structure as an organizing principle for universal Hamiltonian learning
AU - Mingkang Liu
AU - Zhanghao Zhouyin
AU - Guanghui Wang
AU - Daye Zheng
AU - Lei Shen
AU - Qiangqiang Gu
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36135
UR - https://arxiv.org/abs/2610.36135
AB - Density functional theory (DFT) gives the electronic structure of materials, but its cost limits large-supercell calculations and materials screening. Machine-learned Hamiltonians bypass the self-consistent cycle but are usually system-specific; universal ones could cover new compositions and disordered solids. Such models must generalize across chemistry and keep downstream properties physical, while staying inexpensive for large cells. Here we introduce UniTB, a universal E(3) equivariant Hamiltonian representation framework that integrates physical priors rooted in density-functional tight-binding theory with deep learning. UniTB's network, which corrects a prior Hamiltonian, generalizes across chemistry through a mixture of experts routed by that prior and a charge-equilibration head as in self-consistent-charge tight binding. A projection bounds band shifts from the prior, suppressing spurious states and keeping downstream properties physical. We provide the fastest SO(2) tensor-product GPU kernels for the network. The variant UniTB-Flash assembles its prior from two-center tables at O(N) cost for N atoms, against O(Nlog N) on a grid. Trained on 29,242 crystals, UniTB reaches a 0.48 meV matrix-element error on nonmagnetic test crystals spanning 68 elements. Without amorphous training data, both models agree with DFT optics and conductivity of amorphous Ge-Sb-Te. UniTB-Flash ranks candidates with no significant difference from UniTB, whose property values are more accurate; together they screen 16,195 crystals for five application domains of industrial relevance.
ER -