The Structure of the Pairing Interaction in the 2D Hubbard Model

TL;DR

This study uses advanced Monte Carlo simulations to analyze the pairing interactions in the 2D Hubbard model, revealing that magnetic spin exchange channels primarily drive the $d_{x^2-y^2}$ pairing mechanism.

Contribution

It provides a detailed decomposition of the pairing vertex, highlighting the dominant role of magnetic exchange interactions in the pairing process.

Findings

The pairing vertex increases with momentum transfer.

The vertex decreases when energy transfer exceeds the spin susceptibility scale.

Magnetic spin exchange is the main contributor to pairing.

Abstract

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for $d_{x^2-y^2}$ pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the $Q=(\pi, \pi)$ spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.