  We consider the problem of extracting an effective low-energy spin model from
a Kondo Lattice Model (KLM) with classical localized moments. The non-analytic
dependence of the effective spin-spin interactions on the Kondo exchange $J$
excludes the possibility of using perturbation theory beyond the second order
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction at zero temperature. Here we
introduce a Machine Learning (ML) assisted protocol to extract effective two-
and four-spin interactions by integrating out the conduction electrons of the
original KLM. The resulting effective spin model reproduces the phase diagram
obtained with the original KLM as a function of magnetic field and easy-axis
anisotropy and reveals the effective four-spin interactions that are
responsible for the field induced skyrmion crystal phase. Moreover, this
minimal spin model enables an efficient computation of static and dynamical
properties with a much lower numerical cost relative to the original KLM. A
comparison of the dynamical spin structure factor in the fully polarized phase
computed with the effective model and the original KLM reveals a good agreement
for the magnon dispersion despite the fact that this information was not
included in the training data set.
