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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], wepresent in detail the Toulouse-point analytic solution of the two-lead Kondojunction model. The existence and location of the solvable point is notmodified, but the calculational methodology and the final expressions forobservable quantities change markedly as compared to the existent results. Thissolvable point is one of the remarkably few exact results for non-equilibriumtransport in correlated systems. It yields relatively simple analyticalexpressions for the current in the full range of temperature, magnetic fieldand voltage. It also shows precisely, within the limitations of the Toulousefine-tuning, how the transport evolves depending on the relative strengths ofinter-lead and intra-lead Kondo exchange couplings ranging from weak to strong.Thus its improved understanding is an important stepping stone for futureresearch.

Consistent bosonization-debosonization II: The two-lead Kondo problem and the fate of its non-equilibrium Toulouse point