  Quantum Monte Carlo method is used to study the coupled spin-pseudospin
Hamiltonian in one-dimension (1D) that models the charge-ordering instability
of the anisotropic Hubbard ladder at quarter filling. We calculate the
temperature dependence of the uniform spin susceptibility and the spin and
charge excitation spectra of the system to show that there is a parameter and
temperature region where the spin degrees of freedom behave like a 1D
antiferromagnetic Heisenberg model. Anomalous spin dynamics in the disorder
phase of a typical charge-ordered material $\alpha'$-NaV$_2$O$_5$ is thereby
considered.
