microscopic foundation has yet to be carefully examined. Indeed, a formal derivation of the dynamical equation for the order parameter of the Mott transition requires integrating out the microscopic electron and lattice degrees of freedom. This is generally very difficult if not impossible, and phenomenological expressions are often used in the kinetics simulations.

In this paper, we perform the first-ever microscopic simulation of the thermal Mott transition in the Hubbard model by keeping both lattice and electron degrees of freedom. We employ the Langevin molecular dynamics (MD) method to simulate the lattice fluctuations, which provide the relaxation mechanism and the source of stochastic force for the order parameter field. To explicitly include the microscopic correlation effects, the electron degrees of freedom are [*dynamically*]{} integrated out during the MD simulation. This is achieved by solving the Hubbard model using the efficient Gutzwiller method at every MD time-step. We show that the temperature-driven Mott transition is described by the nucleation and growth scenario, consistent with several recent nano-imaging experiments. We further characterize the different stages of the transformation dynamics and the structure of the intermediate mixed-phase states.

The rest of the paper is organized as follows. Section \[sec:GMD\] presents the new quantum 