  The temperature-dependent effective potential (TDEP) method for anharmonic
phonon dispersion is generalized to the full potential case by combining with
path integral formalism. This extension naturally resolves the intrinsic
difficulty in the original TDEP at low temperature. The new method is applied
to solid metallic hydrogen at high pressure. A colossal nuclear quantum effect
(NQE) and subsequent anharmonicity are discovered, which not only leads to
unexpectedly large drift of protons, but also slows down the convergence rate
substantially when computing the phonon dispersions. By employing direct ab
initio path integral molecular dynamics simulations as the benchmark, a
possible breakdown of phonon picture in metallic hydrogen due to colossal NQE
is indicated, implying novel lattice dynamical phenomena might exist. Inspired
by this observation, a general theoretical formalism for quantum lattice
dynamics beyond phonon is sketched, with the main features being discussed.
