Exact Equivariance from Ordinary Neural Networks for Lattice Many-Body Dynamics
Abstract
Large-scale simulations of correlated electron systems require repeated evaluations of the electronic forces and transition energies driving collective dynamics. Machine-learning surrogates alleviate this bottleneck, but incorporating symmetry often involves carefully designed descriptors or specialized network architectures. We show that ordinary multilayer perceptrons equipped with finite-group averaging provide exactly equivariant surrogates directly from microscopic configurations. The construction separates symmetry enforcement from the internal network architecture and applies to both discrete and continuous lattice degrees of freedom. In the Falicov--Kimball model, it predicts directional hopping free-energy differences; in the Holstein model, its invariant limit generates conservative lattice forces. Benchmarks against exact diagonalization establish microscopic accuracy and agreement of dynamical correlations, while large-scale simulations recover multiscale charge ordering and charge-density-wave coarsening. These results demonstrate an accessible, reusable route to symmetry-preserving many-body dynamics for systems with finite lattice point groups.
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BibTeX
@misc{jang2026exact,
title = {{Exact Equivariance from Ordinary Neural Networks for Lattice Many-Body Dynamics}},
author = {Ho Jang and Sankha Subhra Bakshi and Gia-Wei Chern},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27132},
eprint = {2609.27132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27132},
}
RIS
TY - UNPB
TI - Exact Equivariance from Ordinary Neural Networks for Lattice Many-Body Dynamics
AU - Ho Jang
AU - Sankha Subhra Bakshi
AU - Gia-Wei Chern
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.27132
UR - https://arxiv.org/abs/2609.27132
AB - Large-scale simulations of correlated electron systems require repeated evaluations of the electronic forces and transition energies driving collective dynamics. Machine-learning surrogates alleviate this bottleneck, but incorporating symmetry often involves carefully designed descriptors or specialized network architectures. We show that ordinary multilayer perceptrons equipped with finite-group averaging provide exactly equivariant surrogates directly from microscopic configurations. The construction separates symmetry enforcement from the internal network architecture and applies to both discrete and continuous lattice degrees of freedom. In the Falicov--Kimball model, it predicts directional hopping free-energy differences; in the Holstein model, its invariant limit generates conservative lattice forces. Benchmarks against exact diagonalization establish microscopic accuracy and agreement of dynamical correlations, while large-scale simulations recover multiscale charge ordering and charge-density-wave coarsening. These results demonstrate an accessible, reusable route to symmetry-preserving many-body dynamics for systems with finite lattice point groups.
ER -