Exact Finite-Size Spectra in the Kondo Problem and Boundary Conformal Field Theory

TL;DR

This paper derives exact finite-size spectra for quantum impurity models related to the Kondo problem using Bethe ansatz and boundary conformal field theory, confirming critical exponents and discussing applications to critical phenomena.

Contribution

It provides exact finite-size spectra for Kondo-related models and links them to boundary conformal field theory, confirming previous critical exponent results.

Findings

Finite-size spectra obtained from Bethe ansatz.

Surface critical exponents match conformal field theory predictions.

Applications discussed in the context of the orthogonality catastrophe.

Abstract

The exact finite-size spectra for several quantum impurity models related to the Kondo problem are obtained from the Bethe ansatz solutions. Using the finite-size scaling in boundary conformal field theory, we determine various surface critical exponents from the exact spectrum, which accord with those obtained by Affleck and Ludwig with Kac-Moody fusion rules. Some applications to critical phenomena observed in connection with the orthogonality catastrophe are also discussed.