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

Area of Science:

• Materials Science
• Computational Physics
• Condensed Matter Physics

Background:

• Effective Hamiltonians are crucial for simulating phase transitions in polarizable materials.
• Current methods for obtaining Hamiltonian coefficients require tedious generation of distorted structures, especially for high-order terms.

Purpose of the Study:

• To develop and apply a Bayesian optimization-based approach for automated effective Hamiltonian construction.
• To reduce the computational cost associated with sampling potential energy surfaces.
• To enable quantitative atomistic modeling of diffusionless phase transitions.

Main Methods:

• Implementation of a Bayesian optimization strategy for active learning.
• Automated selection of distorted structures to sample potential energy surfaces.
• Application to Barium Titanate (BaTiO3) as a model system.

Main Results:

• The effective Hamiltonian for BaTiO3 was successfully obtained using fewer than 30 distorted structures.
• Monte Carlo simulations reproduced structural phase transition temperatures with less than 10% error compared to experimental values.
• The method demonstrates high efficiency and accuracy.

Conclusions:

• The developed Bayesian optimization approach automates effective Hamiltonian construction for polarizable materials.
• This method significantly reduces the number of structures needed, making simulations more efficient.
• The approach is broadly applicable to other materials and facilitates quantitative atomistic modeling of phase transitions.