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

Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Recent measurements of entanglement-related properties of the Hubbard model using ultracold atoms in optical lattices hint that entanglement could provide the key to understanding open questions of this model. We study the local entropy and the total mutual information across the doping-driven Mott transition in the 2D Hubbard model within plaquette cellular dynamical mean-field theory. We find that these two entanglement-related properties detect the Mott insulating phase, the strongly correlated pseudogap phase, and the metallic phase. Imprinted in the entanglement-related properties we also find the pseudogap to correlated metal first-order transition, its finite temperature critical endpoint, and its supercritical crossovers. Through this footprint we reveal an unexpected interplay of quantum and classical correlations. Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature.
Refs: C. Walsh et al., arXiv:2007.00562 (2020), accepted to PRXQuantum, C. Walsh et al., PRL 122, 067203 (2019)