Maximum Entropy Analytic Continuation for Spectral Functions with Non-Positive Spectral Weight

TL;DR

This paper introduces a novel Maximum Entropy analytic continuation method using auxiliary Green functions to accurately extract spectral weights that can change sign or be complex, especially in complex superconducting systems.

Contribution

It proposes a new MaxEntAux method enabling analytic continuation of spectral functions with sign changes or complex values, applicable to multi-orbital and broken symmetry cases.

Findings

Successfully applied to lead in Eliashberg theory

Recovered spectral functions with sign changes

Extended approach to transport quantities

Abstract

Information about the pairing mechanism for superconductivity is contained in the spectral weight for the anomalous (Gorkov) Green function. In the most general case, this spectral weight can change sign on the positive real axis or even be complex in the presence of broken time-reversal symmetry. This renders impossible the direct analytic continuation with Maximum Entropy methods of numerical results obtained for the anomalous Green function either in Matsubara frequency or in imaginary time. Here we show that one can define auxiliary Green functions that allow one to extract the anomalous spectral weight in the most general multi-orbital spin-singlet or triplet cases with no particular symmetry. As a simple example, we treat the case of lead in Eliashberg theory: Maximum Entropy analytic continuation with auxiliary Green functions (MaxEntAux) allows us to recover spectral functions that change sign on the positive real axis. The approach can be extended to transport quantities.