Topological Melting of Magnetic Stripes and the Emergence of Macroscopic d-wave Superconductivity in the 2D Hubbard Model
Abstract
The exact ground state of the two-dimensional Hubbard model is critical for understanding cuprate superconductivity. Previous numerical studies on narrow cylinders found insulating, static stripes that inherently suppress superconductivity. Here, using constrained-path auxiliary-field quantum Monte Carlo on isotropic lattices up to 24 × 24 sites, we show static stripes are boundary artifacts. The true 2D thermodynamic limit yields a topologically melted fluid of dynamically fluctuating magnetic pockets. Furthermore, we reveal the microscopic real-space origin of cuprate particle-hole asymmetry. Hole doping actively melts the magnetic background, driving a Lifshitz transition that unleashes macroscopic dx2−y2 phase coherence at an optimal x ≈ 0.150−0.200. Conversely, electron doping preserves rigid antiferromagnetic domains, confining carriers to narrow fault lines that optimally saturate early at x ≈ 0.100. By extracting the macroscopic off-diagonal long-range order across both regimes, we perfectly recover the skewed phenomenological superconducting dome. Our parameter-free theoretical curve aligns with empirical Uemura and Božović scaling relations, capturing the underdoped emergence, distinct optimal peaks, the 1/8 anomaly suppression, and overdoped collapse. These results prove that robust d-wave superconductivity is the intrinsic ground state of the pure Hubbard Hamiltonian. Finally, we propose the Topological Magnetic Fluctuation Model (TMFM) as the exact real-space microscopic mechanism of the cuprate superconductors.
Related
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BibTeX
@misc{cho2026topological,
title = {{Topological Melting of Magnetic Stripes and the Emergence of Macroscopic d-wave Superconductivity in the 2D Hubbard Model}},
author = {Jin Hyung Cho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.07634},
eprint = {2606.07634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07634},
}
RIS
TY - UNPB
TI - Topological Melting of Magnetic Stripes and the Emergence of Macroscopic d-wave Superconductivity in the 2D Hubbard Model
AU - Jin Hyung Cho
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2606.07634
UR - https://arxiv.org/abs/2606.07634
AB - The exact ground state of the two-dimensional Hubbard model is critical for understanding cuprate superconductivity. Previous numerical studies on narrow cylinders found insulating, static stripes that inherently suppress superconductivity. Here, using constrained-path auxiliary-field quantum Monte Carlo on isotropic lattices up to 24 × 24 sites, we show static stripes are boundary artifacts. The true 2D thermodynamic limit yields a topologically melted fluid of dynamically fluctuating magnetic pockets. Furthermore, we reveal the microscopic real-space origin of cuprate particle-hole asymmetry. Hole doping actively melts the magnetic background, driving a Lifshitz transition that unleashes macroscopic d_x^2−y^2 phase coherence at an optimal x ≈ 0.150−0.200. Conversely, electron doping preserves rigid antiferromagnetic domains, confining carriers to narrow fault lines that optimally saturate early at x ≈ 0.100. By extracting the macroscopic off-diagonal long-range order across both regimes, we perfectly recover the skewed phenomenological superconducting dome. Our parameter-free theoretical curve aligns with empirical Uemura and Božović scaling relations, capturing the underdoped emergence, distinct optimal peaks, the 1/8 anomaly suppression, and overdoped collapse. These results prove that robust d-wave superconductivity is the intrinsic ground state of the pure Hubbard Hamiltonian. Finally, we propose the Topological Magnetic Fluctuation Model (TMFM) as the exact real-space microscopic mechanism of the cuprate superconductors.
ER -