Role of vertex corrections in the spin-fluctuation mediated pairing mechanism

TL;DR

This paper investigates how vertex corrections affect the electron-spin interaction in a 2D Hubbard model, revealing that these corrections reduce the effectiveness of spin-fluctuation mediated pairing in high-temperature superconductors.

Contribution

It provides a numerical and diagrammatic analysis of vertex renormalization effects, highlighting their impact on pairing interactions in the Hubbard model.

Findings

Vertex decreases with temperature across doping levels.

Effective pairing interaction flattens in strong-correlation regime.

Vertex corrections substantially reduce spin-fluctuation pairing in cuprates.

Abstract

We study numerically and partly diagrammatically the renormalization of the electron-spin interaction or vertex in a two-dimensional one-band Hubbard model with spin-fluctuation momentum transfer ${\vv q}=(\pi,\pi)$. We find that the renormalized electron-spin vertex decreases quite generally with decreasing temperature at all doping densities. As a combination of two concurring effects, i.e. the decrease of the vertex and the increase of the spin susceptibility, the effective pairing interaction increases with lowering temperature in the intermediate-correlation regime, but {\it flattens off} in the strong-correlation regime. Our findings indicate that in the high-T$_c$ cuprates the pairing mediated by antiferromagnetic spin fluctuations is substantially reduced due to vertex corrections.