  A single-hole ground state Ansatz for the two-dimensional t-J model has been
recently studied by the 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 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 order 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 are also discussed.
