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

TL;DR

This paper provides an exact bosonization-refermionization solution for a specific anisotropic two-channel Anderson model, revealing its non-Fermi liquid behavior and energy scales, and establishing a rigorous equivalence with a Fermi-Majorana bi-resonant level model.

Contribution

It introduces a new solvable manifold for the anisotropic two-channel Anderson model and constructs explicit fermionic fields and Klein factors, demonstrating the model's non-Fermi liquid fixed points.

Findings

Identifies two energy scales in the model without external fields.

Shows the model approaches a non-Fermi liquid fixed point with residual entropy.

External fields induce a Fermi-liquid fixed point by quenching impurity entropy.

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 bi-resonant 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 to 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 absence of external fields, two energy scales appear and, as the temperature goes to zero, a non-trivial 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.