Finite-temperature linear conductance from the Matsubara Green function without analytic continuation to the real axis

TL;DR

This paper presents a method to compute finite-temperature linear conductance of quantum impurity models directly from Matsubara Green functions using a continued fraction expansion, avoiding problematic analytic continuation.

Contribution

It introduces a faster converging continued fraction expansion of the Fermi function and demonstrates its effectiveness for calculating conductance without real-axis analytic continuation.

Findings

Faster convergence of the continued fraction expansion compared to traditional methods.

Stable interpolation of Green functions on the imaginary axis improves transport property calculations.

Successful application to the single impurity Anderson model at finite temperatures.

Abstract

We illustrate how to calculate the finite-temperature linear-response conductance of quantum impurity models from the Matsubara Green function. A continued fraction expansion of the Fermi distribution is employed which was recently introduced by Ozaki [Phys. Rev. B 75, 035123 (2007)] and converges much faster than the usual Matsubara representation. We give a simplified derivation of Ozaki's idea using concepts from many-body condensed matter theory and present results for the rate of convergence. In case that the Green function of some model of interest is only known numerically, interpolating between Matsubara frequencies is much more stable than carrying out an analytic continuation to the real axis. We demonstrate this explicitly by considering an infinite tight-binding chain with a single site impurity as an exactly-solvable test system, showing that it is advantageous to calculate transport properties directly on the imaginary axis. The formalism is applied to the single impurity Anderson model, and the linear conductance at finite temperatures is calculated reliably at small to intermediate Coulomb interactions by virtue of the Matsubara functional renormalization group. Thus, this quantum many-body method combined with the continued fraction expansion of the Fermi function constitutes a promising tool to address more complex quantum dot geometries at finite temperatures.