Renormalization of the electron-spin-fluctuation interaction in the t-t'-U Hubbard model

TL;DR

This study uses Quantum Monte Carlo to analyze how electron-spin-fluctuation interactions are renormalized in a 2D Hubbard model, revealing temperature-dependent suppression and effects of next-nearest-neighbor hopping on spin dynamics and pairing interactions.

Contribution

It provides the first detailed Quantum Monte Carlo analysis of the renormalization of the electron-spin-fluctuation vertex in the Hubbard model, including effects of next-nearest-neighbor hopping.

Findings

Renormalized el-sp vertex decreases with temperature at all momentum transfers for t'=0.

Inclusion of t'/t<0 increases spin fluctuation damping, especially in overdoped regimes.

Vertex correction consistently reduces the spin-fermion vertex, aligning with diagrammatic calculations.

Abstract

We study the renormalization of the electron-spin-fluctuation (el-sp) vertex in a two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t') hopping by a Quantum-Monte-Carlo calculation. Our results show that for t'=0, the renormalized el-sp vertex decreases quite generally with decreasing temperature at all spin-fluctuation momentum transfers. The suppression of the el-sp vertex results in a substantial reduction of the effective pairing interaction mediated by antiferromagnetic spin fluctuations in both the intermediate- and strong-correlation regimes. The inclusion of a finite t'/t<0, increases the Landau damping rate of spin fluctuations, especially in the overdoped region. The increased damping rate leads to smaller vertex corrections, in agreement with earlier diagrammatic calculations. Still, the vertex correction reduces the spin-fermion vertex, as at t'=0.