Active learning-based automated construction of Hamiltonian for structural phase transitions: a case study on BaTiO₃

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 BaTiO₃(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.