The development of advanced numerical methods has provided a clear understanding of the mechanisms behind the metal-insulator transition in the half-filled Hubbard model in the limits of weak and strong electronic interactions. However, connecting these two regimes is a tremendous computational challenge, and a complete analysis of the phase diagram is missing.
I will present work that aims at resolving this problem and finding how the two mechanisms bridge at intermediate couplings. To achieve this goal, we study the momentum-resolved spectral function and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations. This allows us to identify the Slater and Heisenberg regimes in the phase diagram that are separated by a crossover region of competing spatial and local electronic correlations. We show that investigating the behavior of the local magnetic moment allows us to explain the formation of the insulating state across the entire phase diagram.
