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arXiv · 2602.20073

Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model

Robin Scholle·Pietro M. Bonetti·Walter Metzner·Demetrio Vilardi
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Abstract

We perform a renormalized mean-field study of the two-dimensional repulsive Hubbard model, focusing on the intricate interplay and possible coexistence of magnetic, charge, and superconducting orders. We improve on conventional mean-field theory by utilizing a renormalization group framework that captures high-energy fluctuations. This method generates effective magnetic and $d$-wave pairing interactions, and allows for an unbiased exploration of coexisting phases at weak and moderate interaction strengths. Unrestricted mean-field calculations of the effective Hamiltonian on large finite lattices are combined with analyses in the thermodynamic limit, revealing a rich phase diagram with extensive regions of coexisting orders. We find that $d$-wave superconductivity coexists with N\'eel order on the electron-doped side. On the hole-doped side, superconductivity is found to coexist with spiral or stripe magnetic orders. Within the stripe ordered region, the superconducting order parameter is spatially modulated, with a period that follows the charge modulation of the stripes. Below van Hove filling, pairing provides the primary energy gain, while the stripe order yields only a small, and hence fragile, additional energy lowering.

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Robin Scholle, Pietro M. Bonetti, Walter Metzner, Demetrio Vilardi. 2026-02-23. Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model. https://arxiv.org/abs/2602.20073

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