HIGHLIGHTS
SUMMARY
To include ionic quantum and thermal fluctuations, the authors adopt the stochastic self-consistent harmonic approximation (SSCHA),[26,27] integrated with an on-the-fly machine learned force_field (MLFF) schem for an efficient and accelerated exploration of the stochastic space. Having tested the accuracy of the MLFF in accounting for the energy versus displacement profile, the authors now address its accuracy in obtaining the free_energy Hessian with respect to the atomic positions, from which one can extract the anharmonic contributions to the phonon frequencies. The occurrence of a ferroelectric transition as a function of . . .
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