Counting statistics for the Anderson impurity model: Bethe ansatz and Fermi liquid study

TL;DR

This paper investigates charge transport statistics in the Anderson impurity model using Fermi liquid theory and Bethe ansatz, deriving exact formulas and exploring Kondo physics signatures in current noise.

Contribution

It provides an exact analytic relation for the full counting statistics generating function and offers a conjecture for its form at finite voltage and interaction strength.

Findings

Derived an exact relation between FCS generating function and self-energy.

Validated approach against known results for non-interacting systems.

Identified a double peaked structure in current noise as a signature of Kondo physics.

Abstract

We study the counting statistics of charge transport in the Anderson impurity model (AIM) employing both Keldysh perturbation theory in a Fermi liquid picture and the Bethe ansatz. In the Fermi liquid approach, the object of our principal interest is the generating function for the cumulants of the charge current distribution. We derive an exact analytic formula relating the full counting statistic (FCS) generating function to the self-energy of the system in the presence of a measuring field. We first check that our approach reproduces correctly known results in simple limits, like the FCS of the resonant level system (AIM without Coulomb interaction). We then proceed to study the FCS for the AIM perturbatively in the Coulomb interaction. By comparing this perturbative analysis with a strong coupling expansion, we arrive at a conjecture for an expression for the FCS generating function at O(V^3) (V is the voltage across the impurity) valid at all orders in the interaction. In the second part of the article, we examine a Bethe ansatz analysis of the current noise for the AIM. Unlike the Fermi liquid approach, here the goal is to obtain qualitative, not quantitative, results for a wider range of voltages both in and out of a magnetic field. Particularly notable are finite field results showing a double peaked structure in the current noise for voltages satisfying eV ~ mu H$. This double peaked structure is the ``smoking gun'' of Kondo physics in the current noise and is directly analogous to the single peak structure predicted for the differential conductance of the AIM.