  Based on three general guiding principles, i.e., no double occupancy
constraint, accurate description of antiferromagnetism at half-filling, and the
precise sign structure of the $t$-$J$ model, a new ground state wave function
has been constructed recently [Weng, New J. Phys. 13, 103039 (2011)]. In this
paper, we specifically study such kind of variational ground state for the
one-hole-doped anisotropic two-leg $t$-$J$ ladder using variational Monte Carlo
(VMC) method. The results are then systematically compared with those recently
obtained by density matrix renormalization group (DMRG) simulation. An
excellent agreement is found between the VMC and DMRG results, including a
"quantum critical point" at the anisotropy parameter
$\alpha=\alpha_c\approx0.7$ (with the parameters $t/J=3$), and the emergence of
charge modulation and momentum (Fermi point) reconstruction at
$\alpha>\alpha_c$ due to the quantum interference of the sign structure. In
particular, the wave function indicates that a Landau's quasiparticle
description remains valid at $\alpha<\alpha_c$ but fails at $\alpha>\alpha_c$
due to the breakdown of the one-to-one correspondence of momentum and
translational symmetry of the hole. The explicit form of the wave function
provides a direct understanding on how the many-body strong correlation effect
takes place non-perturbatively in a doped Mott insulator, which sheds
interesting light on the two-dimensional case where the same type of wave
function was proposed to describe the cuprate superconductor.
