Keldysh effective action theory for universal physics in spin-1/2 Kondo dots

TL;DR

This paper develops a universal Keldysh effective action theory for the spin-1/2 Kondo effect in quantum dots, applicable across all temperatures and voltages, and validates it against numerical methods.

Contribution

It introduces a universal analytical framework for the Kondo effect in quantum dots, bridging different coupling regimes with a single expression and matching numerical results.

Findings

Universal shape of conductance matches numerical results.

At the Kondo voltage, differential conductance is 2/3 of its maximum.

The theory applies to asymmetric Anderson models with U=∞.

Abstract

We present a theory for the Kondo spin-1/2 effect in strongly correlated quantum dots. The theory is applicable at any temperature and voltage. It is based on a quadratic Keldysh effective action parameterized by a universal function. We provide a general analytical form for the tunneling density of states through this universal function for which we propose a simple microscopic model. We apply our theory to the highly asymmetric Anderson model with $U=\infty$ and describe its strong coupling limit, weak coupling limit and crossover region within a single analytical expression. We compare our results with numerical renormalization group in equilibrium and with a real-time renormalization group out of equilibrium and show that the universal shapes of the linear and differential conductance obtained in our theory and in these theories are very close to each other in a wide range of temperatures and voltages. In particular, as in the real-time renormalization group, we predict that at the Kondo voltage the differential conductance is equal to 2/3 of its maximum.