Autocorrelation of the density amplitudes as a function of the sample lag in the Markov chain for LPT (upper panel) and PPT (lower panel). This autocorrelation is estimated from 2000 samples after the warm-up phase. The correlation length of the sampler can be estimated by determining the point when correlations drop below 0.1 for the first time. The annealing with the PPT model does not introduce longer correlations in the density sampler.