Systematic compactification of the two-channel Kondo model. II. Comparative study of scaling and universality

TL;DR

This paper compares the scaling behavior of the compactified two-channel Kondo model with the original, revealing universal flow patterns and clarifying when bosonization simplifications are valid.

Contribution

It provides a comparative analysis of the compactified and original models using Anderson's scaling, highlighting universal behaviors and the conditions for reliable bosonization.

Findings

Universal agreement in flow behavior among models

Limits of concordance in scaling behavior

Guidelines for bosonization validity

Abstract

Following up on the systematic compactification of the two-channel Kondo model (and its multichannel extensions; arXiv:2308.03569 (companion paper I)) and the demonstration of its validity over the past proposal of compactification, we resort to a study of scaling using Anderson's simple poor man's procedure to carry out a comparative study of these two and the original model. By doing so we unveil a universal agreement among the three models in how they flow upon scaling, and suggest the general limits of such a concordance. In this way we further elucidate the conditions under which the standard simplifications implicit in many bosonization-based mappings (particularly of quantum impurity models) can be used reliably, and when the consistent bosonization-debosonization approach is needed.