  The stripe phase, an intertwined order observed in high-temperature
superconductors, is regarded as playing a key role in elucidating the
underlying mechanism of superconductivity, especially in cuprates. Following
Jan Zaanen's early scenario, the full-filled charge stripe can be taken as the
interactive elastic quantum strings of holes, stabilized by $\pi$-phase shifts
between neighboring magnetic domains. However, this scenario is challenging to
explain, particularly in terms of electron pairing, which necessitates hole
pairs. In this work, we propose a new effective model for describing the stripe
phase in the hole-doped $t$-$J_z$ model. With respect to the antiferromagnetic
background, the model comprises three types of color-labeled point-defects
coupling to {an effective} spin field. Comparing with numerical results from
large-scale density matrix renormalization group (DMRG) simulations, we find
semi-quantitative agreement in local hole density, magnetic moment, and the
newly proposed spectrum features of the {effective} spin field. By
systematically analyzing the hole-density distribution and the scaling of
groundstate energy at different system sizes, we determine the effective core
radius and the effective hopping amplitude of the quantum string. Furthermore,
the local pinning field can be finely adjusted to drag the quantum string,
offering a potential method for detecting it in optical lattices.
