  We study the dynamics of spontaneous translation symmetry breaking in
holographic models in presence of weak explicit sources. We show that, unlike
conventional gapped quantum charge density wave systems, this dynamics is well
characterized by the effective time dependent Ginzburg-Landau equation, both
above and below the critical temperature, which leads to a "gapless" algebraic
pattern of metal-insulator phase transition. In this framework we elucidate the
nature of the damped Goldstone mode (the phason), which has earlier been
identified in the effective hydrodynamic theory of pinned charge density wave
and observed in holographic homogeneous lattice models. We follow the motion of
the quasinormal modes across the dynamical phase transition in models with
either periodic inhomogeneous or helical homogeneous spatial structures,
showing that the phase relaxation rate is continuous at the critical
temperature. Moreover, we find that the qualitative low-energy dynamics of the
broken phase is universal, insensitive to the precise pattern of translation
symmetry breaking, and therefore applies to homogeneous models as well.
