  We study the Kondo chain in the regime of high spin concentration where the
low energy physics is dominated by the Ruderman-Kittel-Kasuya-Yosida (RKKY)
interaction. As has been recently shown (A. M. Tsvelik and O. M. Yevtushenko,
Phys. Rev. Lett 115, 216402 (2015)), this model has two phases with drastically
different transport properties depending on the anisotropy of the exchange
interaction. In particular, the helical symmetry of the fermions is
spontaneously broken when the anisotropy is of the easy plane type (EP). This
leads to a parametrical suppression of the localization effects. In the present
paper we substantially extend the previous theory, in particular, by analyzing
a competition of forward- and backward- scattering, including into the theory
short range electron interactions and calculating spin correlation functions.
We discuss applicability of our theory and possible experiments which could
support the theoretical findings.
