The Fermi Edge Singularity and Boundary Condition Changing Operators

TL;DR

This paper applies boundary conformal field theory to analyze the Fermi edge singularity, linking boundary condition changes to impurity problems and solving for Luttinger liquids and multi-channel Kondo systems.

Contribution

It introduces a novel approach connecting boundary condition changing operators to the Fermi edge singularity in impurity models.

Findings

Derived the dimension of boundary operators from ground state energy differences.

Solved the Fermi edge singularity for Luttinger liquids with back-scattering.

Analyzed the multi-channel Kondo problem using conformal mappings.

Abstract

The boundary conformal field theory approach to quantum impurity problems is used to study the Fermi edge singularity, occuring in the X-ray adsorption probablility. The deep-hole creation operator, in the effective low-energy theory, changes the boundary condition on the conduction electrons. By a conformal mapping, the dimension of such an operator is related to the groundstate energy for a finite system with different boundary conditions at the two ends. The Fermi edge singularity is solved using this method, for the Luttinger liquid including back-scattering and for the multi-channel Kondo problem.