  On the basis of the self-consistent phonon theory and the special
displacement method, we develop an approach for the treatment of anharmonicity
in solids. We show that this approach enables the efficient calculation of
temperature-dependent anharmonic phonon dispersions, requiring very few steps
to achieve minimization of the system's free energy. We demonstrate this
methodology in the regime of strongly anharmonic materials which exhibit a
multi-well potential energy surface, like cubic SrTiO$_3$, CsPbBr$_3$,
CsPbI$_3$, CsSnI$_3$, and Zr. Our results are in good agreement with
experiments and previous first-principles studies relying on stochastic
nonperturbative and molecular dynamics simulations. We achieve a very robust
workflow by using harmonic phonons of the polymorphous ground state as the
starting point and an iterative mixing scheme of the dynamical matrix. We also
suggest that the phonons of the polymorphous ground state might provide an
excellent starting approximation to explore anharmonicity. Given the
simplicity, efficiency, and stability of the present treatment to
anharmonicity, it is especially suitable for use with any electronic structure
code and for investigating electron-phonon couplings in strongly anharmonic
systems.
