which remains roughly the same throughout the transition. This result is consistent with picture of two coexisting phases in the intermediate state. As the phase transformation progresses, the delta-peak keeps increasing at the expense of the finite-width distribution at finite $D$. Interestingly, the distribution of the local electron density rather uniform, as demonstrated by its histogram $h(n)$ shown in Fig. \[fig:hist\_db\](b). The on-site electron density $n_i$ is very narrowly distributed around the half-filling with a width $\delta n \lesssim 0.01$, and is dominated by a huge delta-peak at $n = 0.5$, with contributions from both the metallic and Mott regions.

![(Color online) \[fig:hist\_db\] Computed histogram of (a) double-occupancy and (b) on-site electron density at varying Mott volume fraction for the temperature-quench simulations of Fig. \[fig:trace\]. ](hist_db.pdf){width="0.99\columnwidth"}

As the phase transformation progresses, both the number and size of the Mott clusters increase with time. At the late stage of the phase transformation, the Mott clusters start to merge through a process akin to the percolation transition. Of central interest here is the evolution of the cluster-size distribution $n(s, t)$, which is shown in Fig. \[fig:histogram\] for different stages of the phase transformation. For small clusters, it is expected that their distribution 