Physics of Arbitrary Doped Kondo Lattices: from a Commensurate Insulator to a Heavy Luttinger Liquid and a Protected Helical Metal.

We study one-dimensional Kondo Lattices (KL) which consist of itinerant electrons interacting with Kondo impurities (KI) - localized quantum magnetic moments. We focus on KL with isotropic exchange interaction between electrons and KI and with a high KI density. The latter determines the principal role of the indirect interaction between KI for the low energy physics. Namely, the Kondo physics becomes suppressed and all properties are governed by spin ordering. We present a first-ever comprehensive analytical theory of such KL at an arbitrary doping and predict a variety of regimes with different electronic phases. They range from commensurate insulators (at filling factors 1/2, 1/4 and 3/4) to strongly interacting electrons (close to these three special cases) and to an exotic phase of a helical metal. The latter can provide a unique platform for realization of an emergent protection of ballistic transport in the spin-rotation invariant system. Finally, we compare out theory with previously obtained numerical results and discuss possible experiments where the theory could be tested.