  Quantum Monte Carlo and density-matrix renormalization group methods are 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 specific heat as well as the spin and charge excitation
spectra of the system. We thereby show that there is a parameter and
temperature region where the spin degrees of freedom are separated from the
charge degrees of freedom and behave like a 1D antiferromagnetic Heisenberg
model, and that, outside this parameter region and above a crossover
temperature, the spin excitations are largely affected by the charge
fluctuations. We argue that observed anomalous spin dynamics in the disorder
phase of a typical charge-ordered material $\alpha'$-NaV$_2$O$_5$ may possibly
be a consequence of this type of spin-charge coupling.
