  The localization and scattering properties of potential wells or barriers
uniformly moving on a lattice are strongly dependent on the drift velocity
owing to violation of the Galilean invariance of the discrete Schr\"odinger
equation. Here a type of localization-delocalization phase transition of
algebraic type is unravelled, which does not require any kind of disorder and
arises when a power-law potential well drifts fast on a lattice. While for an
algebraic exponent $\alpha$ lower than the critical value $\alpha_c=1$
dynamical delocalization is observed, for $\alpha> \alpha_c$ asymptotic
localization, corresponding to an asymptotic frozen dynamics, is instead
realized. At the critical phase transition point $\alpha_=\alpha_c=1$ an
oscillatory dynamics is found, corresponding to Bloch oscillations. An
experimentally-accessible photonic platform for the observation of the
predicted algebraic phase transition, based on light dynamics in synthetic mesh
lattices, is suggested.
