title: Kinetics of thermal Mott transitions in the Hubbard model
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Introduction {#sec:intro}
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Mott metal-insulator transition (MIT) continues to be an important subject in modern condensed matter physics even after more than sixty years of study [@mott90; @imada98; @dobrosavljevic12]. In particular, the unusual properties of the metallic state near the MIT, sometimes also called the bad metal state [@emery95], have attracted considerable attention both experimentally and theoretically [@limelette03; @bartosch10; @itou17; @pustogow18; @terletska11; @sordi12; @vucicevic15; @jawad15; @lenz16; @imada05]. Conventionally, the effort has been focused on the thermodynamic, optical, magnetic, and transport properties in the vicinity of the Mott transition. These are usually achieved experimentally through bulk or macroscopic measurements. Coupled with the advances in many-body techniques such as the quantum Monte Carlo simulations [@leblanc15; @motta17; @kent18] and the dynamical mean-field theory (DMFT) [@georges96; @kotliar06; @gull11], significant progress has been made toward understanding the microscopic mechanisms and the quantum criticality of the MIT.

An important aspect that has received attention only recently is the [*complexity*]{} of MITs in real materials [@dagotto05]. For example, several near-field spectroscopy and nano-imaging experiments [@bonnell12; @atkin12; @liu17] have revealed highly inhomogeneous electronic states with complex nano-scale textures during the first-order metal-insulator transformation in correlated electron systems 