Tracking the Footprints of Spin Fluctuations: A Multi-Method, Multi-Messenger Approach to the Weak-coupling Regime of the Two-Dimensional Hubbard Model*

The Hubbard model is the paradigmatic model of this field, similar to what the drosophila is to genetics. Despite its simplicity, the Hubbard model presents a formidable challenge to computational and theoretical methods alike.

The work I will talk about, borrowing terminology from astrophysics, represents an extensive ’multi-method, multi-messenger’ assessment of the wealth of computational methods that have been developed in recent years to determine the physical properties of the Hubbard model in two spatial dimensions. These methods range from simple mean-field theory to cutting-edge quantum-field theoretical approaches as dynamical mean field theory and its extensions. Each of these methods is compared to two numerically exact benchmarks provided by diagrammatic Monte Carlo and determinantal quantum Monte Carlo. In approaching the weak coupling regime of this model in such a way, I will elucidate the nature and role of magnetic fluctuations present and explain their implications on the theory of metallic materials with strong magnetic correlations. arXiv:2006.10769