Construction of low energy effective Hamiltonians using supervised machine learning.

A crucial problem in modern physics is to derive a low energy effective model from a given high energy model. While perturbation theory is the most commonly used approach, there are many instances when such expansions break down. We propose a simple supervised machine learning (ML) algorithm to find the low energy spin Hamiltonian for a given labeled energy data-set from a “high energy” s-d model. The spin Hamiltonian obtained from the ML assisted approach reproduces the phase diagram of the s-d model and reveals the effective four-spin interactions that stabilize a magnetic field induced skyrmion crystal even in absence of spin anisotropy.