Nonlocal Correlation Effects in dc and Optical Conductivity of the Hubbard Model

TL;DR

This paper investigates how non-local electronic correlations influence the dc and optical conductivity in the Hubbard model, emphasizing the importance of vertex corrections across the Mott transition.

Contribution

It provides a detailed analysis of the role of spatial correlations and vertex corrections in the conductivity of the Hubbard model near the Mott transition.

Findings

Vertex corrections are crucial for accurate conductivity in the metallic regime.

Vertex corrections diminish for dc conductivity in the Mott insulator.

Vertex corrections remain significant for optical conductivity in the Mott insulator.

Abstract

Conductivity is one of the most direct probes of electronic systems, yet its theoretical description remains challenging in the presence of strong non-local correlations. In this Letter, we analyze the conductivity of the half-filled single-band Hubbard model and identify the role of spatial correlations across the Mott transition. We show that in the correlated metallic regime, an accurate description of the conductivity requires not only the correct spectral function but also the inclusion of complex multi-electron processes encoded in vertex corrections. The crossover to the Mott insulating regime is marked by a vanishing contribution of vertex corrections to the DC conductivity. However, in the Mott insulating case, vertex corrections remain significant for the optical conductivity.