  We argue that in the quarter-filled ladder compound NaV_2O_5 the
quasi-one-dimensional spin system is strongly coupled to a low-energy
antiferroelectric mode of the excitonic type. This mode results from the
interplay between the electron hopping along the rungs of the vanadium two-leg
ladders and the Coulomb repulsion between electrons. The charge ordering
observed in sodium vanadate at T_c = 34K corresponds to the softening of the
antiferroelectric mode. We consider the spin-isospin model, which describes the
spin and low-energy charge degrees of freedom in sodium vanadate. Within this
model we explain the observed anomalous temperature-dependence of the
dielectric susceptibility at T_c and the midinfrared absorption continuum. We
identify the broad structure in the low-energy optical absorption spectrum of
NaV_2O_5 with the continuum formed by two spinons and one low-energy charge
excitation.
