Abelian bosonization approach to quantum impurity problems

TL;DR

This paper introduces an Abelian Bosonization method for analyzing quantum impurity problems, specifically the two channel Kondo model, enabling calculation of correlation functions, boundary fixed points, and spectra with comparisons to Non-Abelian Bosonization.

Contribution

It presents a simplified Abelian Bosonization approach for quantum impurity models, providing new tools for boundary analysis and spectral calculations.

Findings

Identified all boundary fixed points and their symmetries.

Calculated finite size spectra for the models.

Compared Abelian and Non-Abelian Bosonization methods.

Abstract

Using Abelian Bosonization, we develop a simple and powerful method to calculate the correlation functions of the two channel Kondo model and its variants. The method can also be used to identify all the possible boundary fixed points and their maximum symmetry, to calculate straightforwardly the finite size spectra, to demonstrate the physical picture at the boundary explicitly. Comparisons with Non-Abelian Bosonization method are made. Some fixed points corresponding to 4 pieces of bulk fermions coupled to s=1/2 impurity are listed.