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Local Entanglement Entropy at the Mott Metal-Insulator Transition in Infinite Dimensions

We study the critical behavior of the single-site entanglement entropy S at the Mott metal-insulator transition in infinite-dimensional Hubbard model. For this model, the entanglement between a single site and rest of the lattice can be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the numerical solution using exact diagonalization and the analytical one using two-site DMFT gives S-Sc \propto α\log_{2}[(1/2-Dc)/Dc](U-Uc), with Dc the double occupancy at Uc and α< 0 being different on two sides of the transition.