Fig. 4: Infinite-temperature correlation functions shown for a variety of disorder types, strengths, and dimensionalities.
a–d, Infinite-temperature correlation functions: a, 1D, random, L = 100; b, 1D, QP, L = 100; c, 2D, random, L2 = 10 × 10; d, 2D, QP, L2 = 10 × 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.
