Within the Schwinger-boson approach for the t-J model, the single hole problem in a two-dimensional quantum antiferromagnet is studied by using the quantum Bogoliubovde Gennes formalism which treats the distortion of the spin background and quantum spin fluctuations on an equal footing. Several self-trapped localized hole states are found in the distorted spin-background as in the case of an anisotropic Heisenberg model. These localized hole states survive at finite temperatures when the antiferromagnetic order becomes short-ranged. The energy separation between the two lowest states is reduced by considering the spin-background distortion, but it remains finite.
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.