Multi-Method, Multi-Messenger Approaches to Models of Strong Correlations

The Hubbard model is the paradigmatic model for electronic correlations. In this talk I present a general framework for the reliable calculation of its properties, which we coined 'multi-method, multi-messenger' approach. I will illustrate the power of this approach with two recent studies: (i) an extensive synopsis of arguably all available finite-temperature methods for the half-filled Hubbard model on a simple square lattice in its weak-coupling regime and (ii) a complementary subset of those applied to the Hubbard model on a triangular geometry. While the former example fully clarifies the impact of spin fluctuations and tracks it footprints on the one- and two-particle level, the latter exhibits the intriguing interplay of geometric frustration (magnetism) and strong correlations (Mottness). These examples may work as a blueprint for similar future studies of strongly correlated systems.