Disentangling real space fluctuations: The diagnostics of metal-insulator transitions beyond single-particle spectral functions

The destruction of metallicity due to the mutual Coulomb interaction of quasiparticles gives rise to fascinating phenomena of solid state physics such as the Mott metal-insulator transition and pseudogap. A key observable characterizing their occurrences is the single-particle spectral function, determined by the fermionic self-energy. In this paper, we investigate in detail how real space fluctuations are responsible for a self-energy that drives the Mott-Hubbard metal-insulator transition. To this aim, we first introduce a real space fluctuation diagnostics approach to the Hedin equation, which connects the fermion-boson coupling vertex <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>λ</a:mi></a:math> to the self-energy <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi mathvariant="normal">Σ</b:mi></b:math>. Second, by using cellular dynamical mean-field theory calculations, we unambiguously identify nearest-neighbor antiferromagnetic excitations as the leading physical processes responsible for the destruction of metallicity across the transition.