Time correlations in 1D quantum impurity problems

TL;DR

This paper introduces an analytical method using form-factors to compute time-dependent correlations in integrable quantum impurity problems, providing new results for fractional quantum Hall edge tunneling and Kondo model spin correlations at zero temperature.

Contribution

It presents the first analytical calculation of frequency-dependent conductivity and spin spectrum in specific quantum impurity systems using form-factor techniques.

Findings

Calculated $G()$ for fractional quantum Hall edge tunneling.

Derived the spectrum $S()$ for the anisotropic Kondo model.

Provided zero-temperature correlation functions for these systems.

Abstract

We develop in this letter an analytical approach using form- factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity $G(\omega)$ for the tunneling between the edges in the $\nu=1/3$ fractional quantum Hall effect, and the spectrum $S(w)$ of the spin-spin correlation in the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mechanics, both at vanishing temperature.