Extracting spectral properties from Keldysh Green functions

TL;DR

This paper explores extending imaginary-time simulations with real-time data on a Keldysh contour to improve spectral property calculations of quantum systems, enhancing resolution at high energies and accurately capturing low-frequency features.

Contribution

It introduces a method combining imaginary and real-time data in spectral analysis, demonstrating improved resolution and accuracy over traditional approaches.

Findings

Real-time data enhances high-energy spectral resolution.

Imaginary-time data is essential for low-frequency features.

The combined approach outperforms Fourier and Padé methods in tests.

Abstract

We investigate the possibility to assist the numerically ill-posed calculation of spectral properties of interacting quantum systems in thermal equilibrium by extending the imaginary-time simulation to a finite Schwinger-Keldysh contour. The effect of this extension is tested within the standard Maximum Entropy approach to analytic continuation. We find that the inclusion of real-time data improves the resolution of structures at high energy, while the imaginary-time data are needed to correctly reproduce low-frequency features such as quasi-particle peaks. As a nonequilibrium application, we consider the calculation of time-dependent spectral functions from retarded Green function data on a finite time-interval, and compare the Maximum Entropy approach to direct Fourier transformation and a method based on Pad\'e approximants.