One particle spectral function and analytic continuation for many-body implementation in the EMTO method

TL;DR

This paper evaluates and improves the stability of the Padé approximant technique for analytic continuation in the EMTO method, demonstrating its effectiveness in electronic structure calculations and proposing its integration with DMFT.

Contribution

It introduces stability enhancements for the Padé approximant in EMTO calculations and discusses its application to DMFT, advancing computational electronic structure methods.

Findings

Padé approximant stability can be improved with specific modifications.

Analytic continuation quality is validated against density of states in solid hydrogen.

Proposed method integrates Padé approximant with EMTO+DMFT for future applications.

Abstract

We investigate one of the most common analytic continuation techniques in condensed matter physics, namely the Pad\'{e} approximant. Aspects concerning its implementation in the exact muffin-tin orbitals (EMTO) method are scrutinized with special regard towards making it stable and free of artificial defects. The electronic structure calculations are performed for solid hydrogen, and the performance of the analytical continuation is assessed by monitoring the density of states constructed directly and via the Pad\'{e} approximation. We discuss the difference between the \textbf{k}-integrated and \textbf{k}-resolved analytical continuations, as well as describing the use of random numbers and pole residues to analyze the approximant. It is found that the analytic properties of the approximant can be controlled by appropriate modifications, making it a robust and reliable tool for electronic structure calculations. At the end, we propose a route to perform analytical continuation for the EMTO + dynamical mean field theory (DMFT) method.