Self-Consistent Phonon (SCPH) corrected by bubble self-energy

[Zhennan-Lin]

I have a question regarding temperature-dependent phonon dispersion relations. I’ve noticed that the Self-Consistent Phonon (SCPH) theory seems unable to capture phonon softening near critical phase transition temperatures. For example, if my material undergoes a phase transition at 1000 K, the SCPH-calculated phonon spectra at 800 K or 600 K still show no imaginary frequencies (no soft modes). Some papers incorporate bubble self-energy corrections to address this. My questions are:

How essential is it to include bubble self-energy in such cases?

If we rely solely on SCPH-calculated free energy to determine the critical phase transition temperature between two phases, how accurate would this be?