Sub-diffusive spreading and anomalous localization in a 2D Anderson model with off-diagonal nonlinearity

We study the electronic wavepacket dynamic in a two-dimensional lattice under the influence of off-diagonal nonlinearity in the regime of diagonal disorder larger than the crystalline bandwidth. By using numerical calculations of the participation function, the mean square displacement and the return probability, we show that the nonlinearity induces a sub-diffusive spreading of the wavepacket. We also report the existence of an anomalous nonlinear strength at which the wavepacket remains strongly localized.