# Complex Spin Hamiltonian Represented by Artificial Neural Network

arXiv: https://arxiv.org/abs/2110.00724 · HTML: https://mlsanity.com/paper/2110.00724/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 45 references that are in the map.
- First posted on arXiv 2 Oct 2021.

## Builds on (most cited first, 3 of 3)

- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [DScribe: Library of Descriptors for Machine Learning in Materials Science](https://mlsanity.com/paper/1904.08875/) (2019)

## Built on by (most cited first, 4 of 4)

- [A practical guide to machine learning interatomic potentials -- Status and future](https://mlsanity.com/paper/2503.09814/) (2025)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)
- [Spin-Dependent Graph Neural Network Potential for Magnetic Materials](https://mlsanity.com/paper/2203.02853/) (2022)
- [Renormalization-Inspired Effective Field Neural Networks for Scalable Modeling of Classical and Quantum Many-Body Systems](https://mlsanity.com/paper/2502.17665/) (2025)

## Abstract (arXiv)

The effective spin Hamiltonian method is widely adopted to simulate and understand the behavior of magnetism. However, the magnetic interactions of some systems, such as itinerant magnets, are too complex to be described by any explicit function, which prevents an accurate description of magnetism in such systems. Here, we put forward a machine learning (ML) approach, applying an artificial neural network (ANN) and a local spin descriptor to develop effective spin potentials for any form of interaction. The constructed Hamiltonians include an explicit Heisenberg part and an implicit non-linear ANN part. Such a method successfully reproduces artificially constructed models and also sufficiently describe the itinerant magnetism of bulk Fe3GeTe2. Our work paves a new way for investigating complex magnetic phenomena (e.g., skyrmions) of magnetic materials.