The Pairing Interaction in the 2D Hubbard Model

TL;DR

This study uses quantum Monte Carlo methods to analyze the effective pairing interaction in a 2D Hubbard model, revealing its momentum and frequency dependence and its enhancement in the underdoped regime.

Contribution

It characterizes the momentum and frequency dependence of the pairing interaction in the 2D Hubbard model using a dynamic cluster quantum Monte Carlo approach, highlighting the role of exchange energy J.

Findings

The eigenfunction varies as (cos k_x - cos k_y) across the Brillouin zone.

The pairing interaction is attractive for near-neighbor singlet pairs.

The pairing strength increases as the system becomes underdoped.

Abstract

A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a 2D Hubbard model with a near neighbor hopping $t$ and an on-site Coulomb interaction $U$ . The effective pairing interaction is characterized in terms of the momentum and frequency dependence of the eigenfunction of the leading eigenvalue of the irreducible particle-particle vertex. The momentum dependence of this eigenfunction is found to vary as $(\cos k_x-\cos k_y)$ over most of the Brillouin zone and its frequency dependence is determined by the exchange energy $J$. This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by $J^{-1}$. The strength of the pairing interaction measured by the size of the d-wave eigenvalue peaks for $U$ of order the bandwidth $8t$. It is found to increase as the system is underdoped.