TRIQS/Nevanlinna: Implementation of the Nevanlinna Analytic Continuation method for noise-free data

Abstract

We present the TRIQS/Nevanlinna analytic continuation package, an efficient implementation of the methods proposed by J. Fei et al. (2021) [53] and (2021) [55]. TRIQS/Nevanlinna strives to provide a high quality open source (distributed under the GNU General Public License version 3) alternative to the more widely adopted Maximum Entropy based analytic continuation programs. With the additional Hardy functions optimization procedure, it allows for an accurate resolution of wide band and sharp features in the spectral function. Those problems can be formulated in terms of imaginary time or Matsubara frequency response functions. The application is based on the TRIQS C++/Python framework, which allows for easy interoperability with other TRIQS-based applications, electronic band structure codes and visualization tools. Similar to other TRIQS packages, it comes with a convenient Python interface.

Program summary

Program Title: TRIQS/Nevanlinna

CPC Library link to program files: https://doi.org/10.17632/4cbzfy5rds.1

Developer's repository link: https://github.com/TRIQS/Nevanlinna

Licensing provisions: GPLv3

Programming language: C++/Python

External routines/libraries: TRIQS 3.2 [1], Boost >= 1.76.0, Eigen >= 3.4.0, cmake >= 3.20.

Nature of problem: Finite-temperature field theories are widely used to study quantum many-body effects and electronic structure of correlated materials. Obtaining physically relevant spectral functions from results in the imaginary time/Matsubara frequency domains requires solution of an ill-posed analytic continuation problem as a post-processing step.

Solution method: We present an efficient C++/Python open-source implementation of the Nevanlinna/Caratheodory analytic continuation.