Extreme competition between stripes and superconductivity in the hole-doped Hubbard model
Abstract
The two-dimensional Hubbard model was originally proposed as the minimal model of uniform d-wave superconductivity in the cuprate high-temperature superconductors, but recent calculations with relevant parameters in a realistic doping regime have often found other ground states. Further, uncertainty remains over such results due to the intrinsic bias of different computational methods. Here we address this uncertainty through state-of-the-art neural tensor network and neural backflow state simulations, enabled by large-scale GPU computation, that together reach an unprecedented variational accuracy on lattices with up to 1024 sites. At 1/8 doping in the pure Hubbard model, as well as with next-nearest-neighbor hopping relevant to the hole-doped cuprates, we reveal a near degeneracy among a low-energy uniform d-wave state, superconducting stripes, and non-superconducting stripe states on the milli-t energy scale. Our work rebalances the narrative that the Hubbard model supports a single dominant order in relevant parameter regimes towards a picture of extreme competition between stripes and superconductivity.
Related
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- Interplay between Spin Stripes and Pairing Crossover in the Bilayer Hubbard Model
- Superconductivity in the Repulsive Hubbard Model on Different Geometries Induced by Density-Assisted Hopping
- Weyl superconductivity from Feshbach resonance in the three-dimensional repulsive Hubbard model
- A B1g phonon unlocks d-wave superconductivity in the repulsive Hubbard model
BibTeX
@misc{chen2026extreme,
title = {{Extreme competition between stripes and superconductivity in the hole-doped Hubbard model}},
author = {Ao Chen and Johnnie Gray and Si-Jing Du and Garnet Kin-Lic Chan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30321},
eprint = {2610.30321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30321},
}
RIS
TY - UNPB
TI - Extreme competition between stripes and superconductivity in the hole-doped Hubbard model
AU - Ao Chen
AU - Johnnie Gray
AU - Si-Jing Du
AU - Garnet Kin-Lic Chan
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.30321
UR - https://arxiv.org/abs/2610.30321
AB - The two-dimensional Hubbard model was originally proposed as the minimal model of uniform d-wave superconductivity in the cuprate high-temperature superconductors, but recent calculations with relevant parameters in a realistic doping regime have often found other ground states. Further, uncertainty remains over such results due to the intrinsic bias of different computational methods. Here we address this uncertainty through state-of-the-art neural tensor network and neural backflow state simulations, enabled by large-scale GPU computation, that together reach an unprecedented variational accuracy on lattices with up to 1024 sites. At 1/8 doping in the pure Hubbard model, as well as with next-nearest-neighbor hopping relevant to the hole-doped cuprates, we reveal a near degeneracy among a low-energy uniform d-wave state, superconducting stripes, and non-superconducting stripe states on the milli-t energy scale. Our work rebalances the narrative that the Hubbard model supports a single dominant order in relevant parameter regimes towards a picture of extreme competition between stripes and superconductivity.
ER -