We present an Ising-like intermediate phase for one-dimensional Kondo insulator systems. Resulting from a spinon splitting, its low-energy excitations are critical Ising modes, whereas the triplet sector has a spectral gap. It should occur as long as the RKKY oscillation amplitude dominates over any direct exchange between localized spins. The chiral fixed point, however, becomes unstable in the far Infra-Red limit due to prevalent fluctuations among localized spins which induce gapless triplet

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... excitations in the spectrum. Based on previous numerical results, we obtain a paramagnetic disordered state ruled by the correlation length of the single impurity Kondo model.