Exact Fermi-edge singularity exponent in a Luttinger liquid

TL;DR

This paper provides an exact calculation of the Fermi-edge singularity exponent in a one-dimensional Luttinger liquid, confirming boundary fixed point assumptions and relating impurity exponents to Luttinger liquid properties.

Contribution

It presents the exact Fermi-edge singularity exponent for a Luttinger liquid at g=1/2 and explores impurity effects using Abelian bosonization for k=2 and 4.

Findings

Confirmed the open boundary fixed point for g=1/2

Derived orthogonality exponents for Kondo impurities

Linked impurity exponents to Luttinger liquid behavior

Abstract

We report the exact calculation of the Fermi-edge singularity exponent for correlated electrons in one dimension (Luttinger liquid). Focusing on the special interaction parameter g=1/2, the asymptotic long-time behavior can be obtained using the Wiener-Hopf method. The result confirms the previous assumption of an open boundary fixed point. In addition, a dynamic k-channel Kondo impurity is studied via Abelian bosonization for k=2 and k=4. It is shown that the corresponding orthogonality exponents are related to the orthogonality exponent in a Luttinger liquid.