A Lie-Algebraic Approach To the Kondo Problem

TL;DR

This paper applies a Lie-algebraic framework to analyze the Kondo problem, deriving a classical limit for large spin degeneracy and constructing a quantum theory for finite spins, providing new insights into its ground state.

Contribution

It introduces a Lie-algebraic approach to the Kondo problem, connecting classical and quantum descriptions through a renormalized theory for large spin degeneracy.

Findings

Classical limit of the theory as N approaches infinity

Ground state determined for the renormalized classical theory

Quantum theory constructed around the classical limit for finite N

Abstract

The Kondo problem is studied using the unitary Lie algebra of spin-singlet fermion bilinears. In the limit when the number of values of the spin $N$ goes to infinity the theory approaches a classical limit, which still requires a renormalization. We determine the ground state of this renormalized theory. Then we construct a quantum theory around this classical limit, which amounts to recovering the case of finite $N$.