  Following the development of a scheme to bosonize and debosonize consistently
[N. Shah and C.J. Bolech, Phys. Rev B 93, 085440 (2016); arXiv:1508.03078], we
present in detail the Toulouse-point analytic solution of the two-lead Kondo
junction model. The existence and location of the solvable point is not
modified, but the calculational methodology and the final expressions for
observable quantities change markedly as compared to the existent results. This
solvable point is one of the remarkably few exact results for non-equilibrium
transport in correlated systems. It yields relatively simple analytical
expressions for the current in the full range of temperature, magnetic field
and voltage. It also shows precisely, within the limitations of the Toulouse
fine-tuning, how the transport evolves depending on the relative strengths of
inter-lead and intra-lead Kondo exchange couplings ranging from weak to strong.
Thus its improved understanding is an important stepping stone for future
research.
