Emergent nearest-neighbor attraction in the fully renormalized interactions of the single-band repulsive Hubbard model at weak coupling

TL;DR

This paper investigates the effective interactions in the half-filled 2D Hubbard model, revealing emergent non-local nearest-neighbor attraction at low temperatures, which could be crucial for understanding pairing mechanisms.

Contribution

It extends standard RPA resummations to include high-order contributions and uncovers emergent non-local attraction from purely local repulsive interactions.

Findings

Enhanced local repulsive $W_{\uparrow\downarrow}$ interaction

Emergent non-local nearest-neighbor attraction at low temperatures

Absence of screening in the Hubbard interaction

Abstract

We compute the perturbative expansion for the effective interaction $W$ of the half-filled 2-dimensional Hubbard model. We derive extensions of standard RPA resummations that include arbitrarily high order contributions in the $W_{\uparrow\uparrow}$ and $W_{\uparrow\downarrow}$ basis. Using algorithmic tools we explore the static $Q$-dependent interaction as well as the same-time quantity both in momentum- and real-space. We emphasize the absence of screening in the Hubbard interaction where we find an enhanced repulsive local $W_{\uparrow\downarrow}$ with a non-zero attractive $W_{\uparrow\uparrow}$. Finally, starting from only a locally repulsive bare interaction find an emergent non-local nearest-neighbor attraction for low temperatures at sufficiently large values of $U/t$ which may be key to understanding pairing processes in the model.