Spin-Isospin Model of NaV₂O₅

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.