Nevanlinna.jl: A Julia implementation of Nevanlinna analytic continuation

TL;DR

This paper presents Nevanlinna.jl, an open-source Julia implementation of a causality-preserving analytic continuation method based on Nevanlinna interpolants, enabling extraction of real-frequency data from Matsubara axis calculations in correlated materials.

Contribution

It introduces a comprehensive Julia package for Nevanlinna analytic continuation, including features like Hamburger moment problem and smoothing, facilitating theoretical calculations without statistical noise.

Findings

Effective extraction of real-frequency information from Matsubara data

Preserves causality in the analytic continuation process

Applicable to first-principles calculations of correlated materials

Abstract

We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and, by construction, preserves the causality of a response function. For theoretical calculations without statistical noise, this continuation method is a powerful tool to extract real-frequency information from numerical input data on the Matsubara axis. This method has been applied to first-principles calculations of correlated materials. This paper presents its efficient and full-featured open-source implementation of the method including the Hamburger moment problem and smoothing.