Equivariant Neural Networks for Spin Dynamics Simulations of Itinerant Magnets

TL;DR

This paper introduces a new equivariant neural network architecture tailored for large-scale spin dynamics simulations of the Kondo lattice model, effectively capturing lattice and spin rotations.

Contribution

The paper presents a novel tensor-product-based equivariant neural network architecture specifically designed for simulating spin dynamics in itinerant magnets.

Findings

Validation error reduced to less than one-third with the equivariant model.

Successfully reproduces phase transitions of skyrmion crystals.

Demonstrates effective large-scale simulations of spin dynamics.

Abstract

I present a novel equivariant neural network architecture for the large-scale spin dynamics simulation of the Kondo lattice model. This neural network mainly consists of tensor-product-based convolution layers and ensures two equivariances: translations of the lattice and rotations of the spins. I implement equivariant neural networks for two Kondo lattice models on two-dimensional square and triangular lattices, and perform training and validation. In the equivariant model for the square lattice, the validation error (based on root mean squared error) is reduced to less than one-third compared to a model using invariant descriptors as inputs. Furthermore, I demonstrate the ability to reproduce phase transitions of skyrmion crystals in the triangular lattice, by performing dynamics simulations using the trained model.