Algebraic Localization–Delocalization Phase Transition in Moving Potential Wells on a Lattice

The localization and scattering properties of potential wells or barriers uniformly moving on a lattice are strongly dependent on the drift velocity, owing to a violation of the Galilean invariance of the discrete Schrödinger equation. Here a type of localization–delocalization phase transition of algebraic type is unraveled, 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 lower than the critical value dynamical delocalization is observed, for asymptotic localization, corresponding to asymptotic frozen dynamics, is instead realized. At the critical phase transition point 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.