A single-hole ground state ansatz for the two-dimensional t-J model has been recently studied by variational Monte Carlo (VMC) method. Such a doped hole behaves like a ``twisted non-Landau quasiparticle characterized by an emergent quantum number in agreement with exact numerics. In this work, we further investigate the ground state of two holes by VMC. It is found that the two holes strongly attract each other to form a pairing state with a new quantum number the same as obtained by the numerical exact diagonalization (ED) and density matrix renormalization group (DMRG) calculations. A unique feature of this pairing state is a dichotomy in the pairing symmetry, i.e., a d-wave in terms of the electron c-operators and an s-wave in terms of the new quasiparticles, as explicitly illustrated in the ground state wave function. A similar VMC study of a two-hole wave function for the t-J two-leg ladder also yields a good agreement with the DMRG result. We demonstrate that the pairing mechanism responsible for the strong binding here is not due to the long-range antiferromagnetic nor the resonating-valence-bound pairing in the spin background, but is the consequence of the quantum phase strings created by the hopping of holes. The resulting spin current pattern mediating the pairing force is explicitly illustrated in the VMC calculation. Physical implications to superconductivity at finite doping will be also discussed.
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