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

Daria Gazizova; J. P. F. LeBlanc

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arXiv · 2307.02360

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

Daria Gazizova·J. P. F. LeBlanc

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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.

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Daria Gazizova, J. P. F. LeBlanc. 2023-07-05. Emergent nearest-neighbor attraction in the fully renormalized interactions of the single-band repulsive Hubbard model at weak coupling. https://arxiv.org/abs/2307.02360

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