For the $t\text{−}J$ model, variational wave functions can generally be constructed based on an accurate description of antiferromagnetism (AFM) at half-filling and an exact phase-string sign structure under doping. The single-hole-doped and two-hole-doped states, as determined by variational Monte Carlo (VMC) simulations, display sharply contrasting behaviors. The single-hole state constitutes a “cat state” that resonates strongly between a quasiparticle component and a local loop-current component, with approximately equal weights. In the ground state, the quasiparticle spectral weight $Z_{\mathbf{k}}$ peaks at momenta ${\mathbf{k}}_0\equiv (\pm \frac{\pi }{2},\pm \frac{\pi }{2})$. The total-energy dispersion versus $\mathbf{k}$ agrees remarkably well with the Green function Monte Carlo results throughout the Brillouin zone. However, Landau's one-to-one correspondence hypothesis for quasiparticles breaks down here with the incoherent component exhibiting intrinsic magnetization originating from a minimal $2\times 2$ loop current that forms a $4\times 4$ pattern on the square lattice—a finding in excellent agreement with density matrix renormalization group (DMRG) calculations. In the two-hole ground state, a new pairing mechanism is revealed: the two holes are automatically fused into a tightly bound object consisting of an incoherent $d_{xy}$ pairing along the diagonal direction by compensating the local loop currents. This hole pair is again a “cat state” that resonates strongly between the incoherent $d_{xy}$ and a coherent $d_{x^2-y^2}$ Cooper channel to gain substantial hopping energy. Its size extends over an area of about $4\times 4$ lattice spacings, much smaller than the divergent AFM correlation length, implying that it should survive as a minimal superconducting building block even in the dilute doping regime. Experimental implications and the generalization to the finite-doping case are briefly addressed.

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• Holon
• Spinon
• Superconductivity
• Strongly correlated systems
• Monte Carlo methods
• t-J model