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 $24 \times 24$ 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 $x \approx 0.150-0.200$. Conversely, electron doping preserves rigid antiferromagnetic domains, confining carriers to narrow fault lines that optimally saturate early at $x \approx 0.100$. 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 Bo\v{z}ovi\'c 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.