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

TL;DR

This paper explores how real space fluctuations influence the self-energy leading to the Mott metal-insulator transition, introducing a new diagnostic approach and identifying key physical processes through advanced calculations.

Contribution

It introduces a real space fluctuation diagnostics method for the Hedin equation and applies cellular dynamical mean-field theory to identify processes driving the transition.

Findings

Real space fluctuations significantly impact the self-energy near the transition.

The diagnostics approach reveals dominant physical processes causing metallicity destruction.

Cellular dynamical mean-field theory clarifies the role of fluctuations in the Mott transition.

Abstract

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 the 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 $\lambda$ to the self-energy $\Sigma$. Second, by using cellular dynamical mean-field theory calculations for $\lambda$ we identify the leading physical processes responsible for the destruction of metallicity across the transition.