Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain

We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, $Z_2$ symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localization.

Figure 1

Transformation from the frame of the vector $\mathbf{S}$ to that of $\overrightarrow{\mathcal{S}}$. Angles ${\alpha }_{\parallel ,\perp }$ define the modulus of the “transverse” component ${\overrightarrow{\mathcal{S}}}_{\perp }$ and its rotation around the “longitudinal” component ${\overrightarrow{\mathcal{S}}}_{\parallel }$, respectively.