Bosonization approach to the mixed-valence two-channel Kondo problem

Abstract

We present in detail the bosonization-refermionization solution of the anisotropic version of the two-channel Anderson model at a particular manifold in the space of parameters of the theory, where we establish an equivalence with a Fermi-Majorana biresonant-level model. The correspondence is rigorously proved by explicitly constructing the new fermionic fields and Klein factors in terms of the original ones and showing that the commutation properties between original and new Klein factors are of semionic type. We also demonstrate that the fixed points associated with the solvable manifold are renormalization-group stable and generic, and therefore representative of the physics of the original model. The simplicity of the solution found allows for the computation of the full set of thermodynamic quantities. In particular, we compute the entropy, occupation, and magnetization of the impurity as functions of temperature, and identify the different physical energy scales. In the absence of external fields, two energy scales appear and, as the temperature goes to zero, a nontrivial residual entropy indicates that the model approaches a universal line of fixed points of non-Fermi-liquid type. An external field, even if small, introduces a third energy scale and causes the quenching of the impurity entropy to zero, taking the system to a corresponding Fermi-liquid fixed point.

Consistent bosonization-debosonization. I. A resolution of the nonequilibrium transport puzzle

“…We anticipate no subtleties coming from these, but we carry out a careful treatment nevertheless so as to show that explicitly. The most rigorous way to proceed is by identifying relations between different bilinears of old and new Klein factors, and fixing the four arbitrary phases that appear [31][32][33]:…”

“…We will now, on the one hand, combine the exponentials in which the bosons appear with the same sign (we are prompted to do this by a study of the corresponding operator product expansions, OPEs, and by the consistency with the mapping of the Klein factors [31,32]). On the other hand, we will be careful not to combine the exponentials in which the bosonic exponents appear with opposite signs (prompted by the suspicion, from our perturbative analysis, that the ν = c, s sectors should not completely decouple from the tunneling process).…”

“…Here we follow the procedure and notations as in Ref. 32. We will use, for convenience, a Nambu structure [otherwise we need to introduce sgn (ω n ) in the diagonal entries], but we do not need to use Keldysh and, instead, we will use Matsubara formalism and the following spinor basis:…”

Consistent bosonization-debosonization. II. The two-lead Kondo problem and the fate of its nonequilibrium Toulouse point

“…The same as in the case of the simple barrier junction, we do not expect the Klein factors to modify the physics. We treat them as we did in that case [28,29] by identifying relations between different bilinears of original and new Klein factors and fixing the four arbitrary phases; see Eqs. (16a)-(16d) from Ref.…”

Solvable limit for the SU(N) Kondo model

“…More over, one can also show 22,23 that the remaining Klein factors can be absorbed into the impurity part of the Hamiltonian. Hence, from here on the Klein factors are not retained explicitly for further calculations.…”