Relativistic Strongly Correlated Theories for Solid-State Applications

In weakly correlated electron systems, the direct Coulomb interaction can be modeled by an effective single-particle potential, e.g., Density Functional Theory. When strong correlations dominate, these mean-field theories can be used as a reference state for various strongly correlated approaches. Relativistic effects are typically added perturbatively, but this is not adequate for systems composed of heavy elements and the vast unexplored space of strongly topological materials. This requires us to adjust existing theories to account for a Dirac reference state by carefully re-evaluating current methodologies to account for four component spinors and additional electron-electron interactions, e.g., Breit and Gaunt terms. Here, we present a Coupled-Cluster Theory using a Dirac-Hartree-Fock reference state for variety of molecular and solid states systems. Emphasis will be given of new features not accounted for in a non-relativistic framework and implications for solid-state applications.