Pairing Glue in the Hubbard and t-J Models

TL;DR

This paper investigates whether the pairing interaction in the Hubbard and t-J models acts as an instantaneous or retarded 'glue', based on numerical studies of the underlying dynamics and energy scales involved.

Contribution

The study provides numerical evidence clarifying whether the pairing interaction in these models is instantaneous or mediated by retarded spin fluctuations.

Findings

Interaction is consistent with an instantaneous exchange coupling J.

Spectrum aligns with the Mott gap energy scale.

Results suggest a non-retarded, exchange-based pairing mechanism.

Abstract

The question of whether one should speak of a "pairing glue" in the Hubbard and t-J models is basically a question about the dynamics of the pairing interaction. If the dynamics of the pairing interaction arises from virtual states, whose energies correspond to the Mott gap, and give rise to the exchange coupling J, the interaction is instantaneous on the relative time scales of interest. In this case, while one might speak of an "instantaneous glue", this interaction differs from the traditional picture of a retarded pairing interaction. However, if the energies correspond to the spectrum seen in the dynamic spin susceptibility, then the interaction is retarded and one speaks of a spin-fluctuation glue which mediates the d-wave pairing. Here we present results from numerical studies which provide insight into this question.