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We study numerically the phase diagram and the response under a driving forceof the phase field crystal model for pinned lattice systems introduced recentlyfor both one and two dimensional systems. The model describes the latticesystem as a continuous density field in the presence of a periodic pinningpotential, allowing for both elastic and plastic deformations of the lattice.We first present results for phase diagrams of the model in the absence of adriving force. The nonlinear response to a driving force on an initially pinnedcommensurate phase is then studied via overdamped dynamic equations of motionfor different values of mismatch and pinning strengths. For large pinningstrength the driven depinning transitions are continuous, and the slidingvelocity varies with the force from the threshold with power-law exponents inagreement with analytical predictions. Transverse depinning transitions in themoving state are also found in two dimensions. Surprisingly, for sufficientlyweak pinning potential we find a discontinuous depinning transition withhysteresis even in one dimension under overdamped dynamics. We alsocharacterize structural changes of the system in some detail close to thedepinning transition.

Nonlinear Driven Response of a Phase-Field Crystal in a Periodic Pinning Potential