Maximum entropy analytic continuation of anomalous self-energies

TL;DR

This paper introduces a novel maximum entropy analytic continuation method for anomalous self-energies in superconductors, enabling the extraction of sign-changing spectral functions from numerical data.

Contribution

It proposes an auxiliary self-energy approach that ensures non-negative spectral weight, allowing standard maximum entropy methods to analyze sign-changing spectra.

Findings

Successfully applied to K3C60 superconducting state

Proven analytically and numerically that the auxiliary function has non-negative spectral weight

Enables analysis of pairing glue in superconductors with sign-changing spectra

Abstract

The anomalous self-energy plays an important role in the analysis of superconducting states. Its spectral weight provides information on the pairing glue of superconductors, but it can change in sign. In many numerical approaches, for example Monte Carlo methods based on the Nambu formalism, the anomalous self-energy is obtained on the Matsubara axis, and nonpositive spectral weight cannot be directly obtained using the standard maximum entropy analytic continuation method. Here, we introduce an auxiliary self-energy corresponding to a linear combination of the normal and anomalous self-energies. We analytically and numerically prove that this auxiliary function has non-negative spectral weight independent of the pairing symmetry, which allows to compute the sign-changing spectrum of the original self-energy using the maximum entropy approach. As an application, we calculate the momentum-resolved spectral function of K$_3$C$_{60}$ in the superconducting state.