Exact non-linear I-V curve near two-channel Kondo-Luttinger quantum critical point

It has been known since 1990's that a Kondo impurity coupled to Luttinger liquid wire undergoes an exotic quantum phase transition with decreasing Luttinger parameter K (or increasing electron interactions) from the 1-channel to 2-channel Kondo ground states at K=1/2. However, the quantum critical properties near this transition is still not known to date due to lack of controlled theoretical tools to examine the physics near the strong coupling 2-channel Kondo fixed point. In this paper, we address this long-standing issue via bosonization-refermionization approach near 2-channel Kondo state. We overcome the problem by mapping the system at the Toulouse point onto an effective two-lead free fermion model subject to a local tunneling. Remarkably, the non-equilibrium transport of the system is exactly solvable in this limit. An analytic form for the non-linear differential conductance is obtained. Our results offer an unique example of exactly and analytically accessible non-equilibrium transport near a quantum critical point; they are relevant for the recent experiment in a dissipative Kondo dot.