Information-theoretic description of superconductivity in a doped Mott insulator*

Quantum information can be used to advance our understanding of phases of matter in many-body quantum systems. We use tools of quantum information to characterize the entanglement-related properties of unconventional superconductivity in a doped Mott insulator. We study the two-dimensional Hubbard model with cluster dynamical mean-field theory to show how key measures of correlations -local entropy, thermodynamic entropy and total mutual information- detect the superconducting phase obtained upon doping the Mott insulating phase. We find that the behavior of the difference in the local entropy between the normal and superconducting states follows that of the potential energy. In the superconducting state thermodynamic entropy is strongly suppressed near the Mott insulator, whereas the total mutual information is amplified and shows a peak versus doping.