2D, QP, L^2 = 10 x 10; Grey dot-dashed vertical lines indicate the approximate timescale beyond which accuracy cannot be guaranteed. However, the results typically remain reasonable until much longer timescales. Black dashed lines show the long-time average computed directly without explicit time evolution, which is valid at strong (quasi)disorder only. The results are averaged over Ns [50, 128] disorder realizations. Error bars indicate the variance over disorder realizations. For both D = 1 and D = 2, the QP potential exhibits most much robust localization at large values of d / J , but by contrast also exhibits more complete thermalization at low values of d / J due to the underlying single-particle phase transition at d / J = 2.
