Exact solutions of Kondo problems in higher-order fermions

TL;DR

This paper develops an exact conformal field theory approach to solve Kondo problems in systems with higher-order fermions, overcoming limitations of previous linearization methods and enabling precise thermodynamic analysis.

Contribution

It introduces a new CFT technique that exactly solves Kondo problems in higher-order fermion systems without linearization, expanding theoretical tools for complex quantum materials.

Findings

Exact solutions for Kondo problems in higher-order fermion systems.

Rigorous bosonization of the entire energy spectrum.

Enhanced ability to evaluate thermodynamic quantities at finite temperatures.

Abstract

The conformal field theory (CFT) approach to Kondo problems, originally developed by Affleck and Ludwig (AL), has greatly advanced the fundamental knowledge of Kondo physics. The CFT approach to Kondo impurities is based on a necessary approximation, i.e., the linearization of the low-lying excitations in a narrow energy window about the Fermi surface. This treatment works well in normal metal baths, but encounters fundamental difficulties in systems with Fermi points and high-order dispersion relations. Prominent examples of such systems are the recently-proposed topological semimetals with emergent higher-order fermions. Here, we develop a new CFT technique that yields exact solutions to the Kondo problems in higher-order fermion systems. Our approach does not require any linearization of the low-lying excitations, and more importantly, it rigorously bosonizes the entire energy spectrum of the higher-order fermions. Therefore, it provides a more solid theoretical base for evaluating the thermodynamic quantities at finite temperatures. Our work significantly broadens the scope of CFT techniques and brings about unprecedented applications beyond the reach of conventional methods.