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Tools of quantum information theory offer a new perspective to characterizephases and phase transitions in interacting many-body quantum systems. TheHubbard model is the archetypal model of such systems and can explain richphenomena of quantum matter with minimal assumptions. Recent measurements ofentanglement-related properties of this model using ultracold atoms in opticallattices hint that entanglement could provide the key to understanding openquestions of the doped Hubbard model, including the remarkable properties ofthe pseudogap phase. These experimental findings call for a theoreticalframework and new predictions. Here we approach the doped Hubbard model in twodimensions from the perspective of quantum information theory. We study thelocal entropy and the total mutual information across the doping-driven Motttransition within plaquette cellular dynamical mean-field theory. We find thatupon varying doping these two entanglement-related properties detect the Mottinsulating phase, the strongly correlated pseudogap phase, and the metallicphase. Imprinted in the entanglement-related properties we also find thepseudogap to correlated metal first-order transition, its finite temperaturecritical endpoint, and its supercritical crossovers. Through this footprint wereveal an unexpected interplay of quantum and classical correlations. Our workshows that sharp variation in the entanglement-related properties and notbroken symmetry phases characterizes the onset of the pseudogap phase at finitetemperature.

Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model