Mott is Different: An Information Theory Description of Mott Physics

This thesis brings an information-theoretic perspective to strongly correlated electron physics problems. Using the paradigmatic model of interacting systems capturing the competition between kinetic and potential energy, the Hubbard model, in two dimensions on a 2 × 2 square lattice, entropy-based quantities are used to characterise the phases of the model as a function of doping. These quantities are analysed in the Mott insulating phase, through the strongly correlated pseudogap phase and correlated metallic phase, and in the superconducting phase. The local entropy and mutual information are found to exhibit an inflection at the endpoint of the pseudogap-correlated metal transition that is continuously connected to the Mott transition at zero doping, a signature of Mott physics extending away from half filling. The inflections trace out a crossover line from the endpoint. In the superconducting phase, the local entropy is found to reflect the source of the superconducting condensation energy, whilst the total mutual information reveals amplified quantum and classical correlations within the superconducting dome. Thermodynamic measures including the thermodynamic entropy and the velocity of sound are also characterised across the pseudogap to correlated metal transition, contributing to the body of work studying cuprate systems - for which the Hubbard model is a minimal model. The thermodynamic entropy in the normal state exhibits a broad maximum that is obliterated in the superconducting phase. The velocity of sound exhibits sharp dips as a function of doping and interaction, arising from Mott physics. Finally, the probability of the eigenstates of the 2 × 2 plaquette in the superconducting state is analysed. These works are presented in a series of four co-authored publications accepted to PRX Quantum [1], PNAS [2], and PRB [3,4]. The results and predictions presented in this thesis could be tested with optical lattice experiments with ultracold atomic gases, and contribute to an understanding of cuprate high temperature superconductors.