Effects of vertex corrections on diagrammatic approximations applied to the study of transport through a quantum dot

TL;DR

This paper investigates how vertex corrections influence diagrammatic approximations in calculating quantum dot conductance, revealing the importance of these corrections for accurate transport modeling in Kondo and mixed valence regimes.

Contribution

It compares NCA and OCA methods, highlighting the significance of vertex corrections in accurately describing quantum dot transport phenomena.

Findings

Vertex corrections are crucial for accurate transport description.

OCA better captures universal scaling properties.

Neglecting vertex corrections leads to significant inaccuracies.

Abstract

In the present work, we calculate the conductance through a single quantum dot weakly coupled to metallic contacts. We use the spin-1/2 Anderson model to describe the quantum dot, while considering a finite Coulomb repulsion. We solve the interacting system using the non-crossing-approximation (NCA) and the one-crossing approximation (OCA). We obtain the linear response conductance as a function of temperature and energy position of the localized level. From the comparison of both approximations we extract the role of the vertex corrections, which are introduced in the OCA calculations and neglected in the NCA scheme. As a function of the energy position, we observe that the diagrams omitted within NCA are really important for appropriately describing transport phenomena in Kondo systems as well as in the mixed valence regime. On the other hand, as a function of temperature, the corrections introduced by OCA partly recover the universal scaling properties known from numerical approaches such as the Numerical Renormalization Group(NRG).