Active learning-based automated construction of Hamiltonian for structural phase transitions: a case study on BaTiO.

The effective Hamiltonians have been widely applied to simulate the phase transitions in polarizable materials, with coefficients obtained by fitting to accurate first-principles calculations. However, it is tedious to generate distorted structures with symmetry constraints, in particular when high-ordered terms are considered. In this work, we implement and apply a Bayesian optimization-based approach to sample potential energy surfaces, automating the effective Hamiltonian construction by selecting distorted structures via active learning. Taking BaTiO(BTO) as an example, we demonstrate that the effective Hamiltonian can be obtained using fewer than 30 distorted structures. Follow-up Monte Carlo simulations can reproduce the structural phase transition temperatures of BTO, comparable to experimental values with an error<10%. Our approach can be straightforwardly applied on other polarizable materials and paves the way for quantitative atomistic modelling of diffusionless phase transitions.