On the applicability of an equation of motion method at low-temperatures: comments on cond-mat/0309458 and cond-mat/0308413

TL;DR

This paper critiques the use of the equation of motion method for low-temperature transport calculations in quantum dots, highlighting its limitations and potential misinterpretations of Fermi-liquid behavior.

Contribution

It demonstrates that the EOM self-energy with a finite cluster can produce spurious singularities, leading to incorrect conclusions about low-temperature physics.

Findings

EOM method can produce artificial singularities at low energies.

Naive application of EOM may misrepresent Fermi-liquid properties.

Correct interpretation requires careful analysis of the self-energy.

Abstract

The equation of motion method (EOM) is one of the approximations to calculate transport coefficients of interacting electron systems. The method is known to be useful to examine high-temperature properties. However, sometimes a naive application of the EOM fails to capture an important physics at low-energy scale, and it happens in recent preprints cond-mat/0309458 and cond-mat/0308413 which study a series of quantum dots. These preprints concluded that a unitarity-limit transport due to the Kondo resonance, which has been deduced from a Fermi-liquid behavior of the self-energy at T=0, $\omega=0$ [A.O., PRB {\bf 63}, 115305 (2001)], does not occur. We show that the EOM self-energy obtained with a finite cluster has accidentally a singular $1/\omega$ dependence around the Fermi energy, and it misleads one to the result incompatible with a Fermi-liquid ground state.