[@qazilbash07; @liu13; @madan15; @lupi10; @qzailbash11; @mcleod16; @stinson18; @mattoni16; @ronchi18; @preziosi18; @singer18]. In fact, MIT in most functional materials, such as vanadium dioxide, is [*discontinuous*]{} at ambient conditions. Understanding the structural and dynamical properties of the mesoscopic patterns during the first-order MIT is not only of fundamental interest, but also has important technological implications.

In the past decade, considerable experimental effort has been devoted to understand the properties of the heterogeneous electronic states in the vicinity of the Mott transition. For instance, the nano-scale phase separation in several temperature-driven MITs was shown to be consistent with the nucleation and percolation scenario [@qazilbash07; @lupi10; @mcleod16; @liu13], similar to that observed in the colossal magnetoresistant materials (CMR) [@uehara99; @fath99; @zhang02]. On the theoretical side, however, a [*microscopic*]{} modeling of these emergent dynamical textures is still lacking. The difficulty is partly due to the multiscale and multi-faceted nature of the MIT kinetics. On one hand, large-scale dynamical simulation is required in order to describe the complex structures of the mixed-phase states in the Mott transition. On the other hand, accurate modeling of the electron correlation effects requires advanced many-body techniques [@leblanc15; @motta17; @kent18; @georges96; @kotliar06; @gull11], most of which are computationally too expensive to 