Possible Cooper instabilities in pair Green functions of the two-dimensional Hubbard model

TL;DR

This paper investigates potential pairing instabilities in the two-dimensional Hubbard model by analyzing Green functions, revealing doping-dependent gaps and providing a method to calculate the gap magnitude without a cutoff.

Contribution

It identifies possible Cooper-like instabilities in the Hubbard model's Green functions and relates the gap to pole locations, offering a new approach to estimate the gap without a cutoff.

Findings

Instabilities exist between 0.03 and 0.24 hole doping.

Maximum gap is approximately 0.08 for U/t=10.

Gap calculation does not require an explicit cutoff.

Abstract

In analogy with ordinary BCS superconductivity, we identify possible pairing instabilities with poles in a certain class of Green functions of the two-dimensional repulsive Hubbard model, which normally signify bound states. Relating the gap to the location of these poles, we find that these instabilities exist in the range of hole doping between 0.03 and 0.24. The magnitude of the gap can be calculated without introducing an explicit cut-off, and for reasonably large coupling U/t = 10, the maximum gap is on the order of 0.08 in units of the hopping parameter t.