Efficient construction of effective Hamiltonians with a hybrid machine learning method

TL;DR

This paper introduces the Lasso-GA Hybrid Method (LGHM), a new approach combining Lasso regression and genetic algorithms to efficiently construct effective Hamiltonian models for complex systems, validated on magnetic materials.

Contribution

The paper presents LGHM, a novel hybrid machine learning method that automates and accelerates the construction of effective Hamiltonians for various physical systems.

Findings

Successfully identified key interaction terms in magnetic materials

Reproduced experimental magnetic ground states and Curie temperatures

Revealed significant interactions influencing magnetic properties

Abstract

The effective Hamiltonian method is a powerful tool for simulating large-scale systems across a wide range of temperatures. However, previous methods for constructing effective Hamiltonian models suffer from key limitations: some require to manually predefine interaction terms limited flexibility in capturing complex systems, while others lack efficiency in selecting optimal interactions. In this work, we introduce the Lasso-GA Hybrid Method (LGHM), a novel approach that combines Lasso regression and genetic algorithms to rapidly construct effective Hamiltonian models. Such method is broadly applicable to both magnetic systems (e.g., spin Hamiltonians) and atomic displacement models. To verify the reliability and usefulness of LGHM, we take monolayer CrI_3 and Fe_3 GaTe_2 as examples. In both cases, LGHM not only successfully identifies key interaction terms with high fitting accuracy, but also reproduces experimental magnetic ground states and Curie temperatures with further Monte Carlo simulations. Notable, our analysis of monolayer Fe_3 GaTe_2 reveals that the single-ion anisotropy and Heisenberg interaction lead to an out-of-plane ferromagnetic ground state, while the fourth-order interactions contribute significantly to the high Curie temperature. Our method is general so it can be applied to construct other effective Hamiltonian models.