Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model
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 -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 -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.
Cite
@article{arxiv.2602.20073,
title = {Coexisting magnetic, charge, and superconducting orders in the two-dimensional Hubbard model},
author = {Robin Scholle and Pietro M. Bonetti and Walter Metzner and Demetrio Vilardi},
journal= {arXiv preprint arXiv:2602.20073},
year = {2026}
}