Kondo Problem and Related One-Dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory

TL;DR

This paper reviews exact solutions for Kondo impurity systems using Bethe-ansatz and boundary conformal field theory, highlighting universal low-energy behaviors and critical properties in one-dimensional quantum systems.

Contribution

It provides a comprehensive review of Bethe-ansatz solutions and boundary conformal field theory applications to the Kondo problem, emphasizing universal aspects and finite-size scaling.

Findings

Finite-size spectra characterize low-energy fixed points.

Universal relations connect Kondo and impurity effects.

Exact critical properties are derived from Bethe-ansatz solutions.

Abstract

We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.