ACTest: A testing toolkit for analytic continuation methods and codes

ACTest is an open-source toolkit developed in the Julia language. Its central goal is to automatically establish analytic continuation testing datasets, which include a large number of spectral functions and the corresponding Green's functions. These datasets can be used to benchmark various analytic continuation methods and codes. In ACTest, the spectral functions are constructed by a superposition of randomly generated Gaussian, Lorentzian, δ-like, rectangular, and Rise-And-Decay peaks. The spectra can be positive definite or non-positive definite. The corresponding energy grids can be linear or non-linear. ACTest supports both fermionic and bosonic Green's functions on either imaginary time or Matsubara frequency axes. Artificial noise can be superimposed on the synthetic Green's functions to simulate realistic Green's functions obtained by quantum Monte Carlo calculations. ACTest includes a standard testing dataset, namely ACT100. This built-in dataset contains 100 testing cases that cover representative analytic continuation scenarios. Now ACTest is fully integrated with the ACFlow and MiniPole toolkits. It can directly invoke the analytic continuation methods as implemented in the ACFlow and MiniPole toolkits for calculations, analyze calculated results, and evaluate computational efficiency and accuracy. ACTest comprises many examples and comprehensive documentation. The purpose of this paper is to introduce the major features and usages of the ACTest toolkit. The benchmark results on the ACT100 dataset for the maximum entropy method, which is probably the most popular analytic continuation method, are also presented.

Program summary

Program title: ACTest

CPC Library link to program files: https://doi.org/10.17632/xvt3wzgt65.1

Developer's repository link: https://github.com/huangli712/ACTest

Licensing provisions: GPLv3

Programming language: Julia

Nature of problem: Analytic continuation is an essential step in quantum many-body computations. It enables the extraction of observable spectral functions from imaginary time or Matsubara frequency Green's functions. Though numerous methods for analytic continuation were proposed, they have not been systematically and fairly benchmarked due to the lack of testing software and datasets.

Solution method: At first, a few peaks (features) are generated randomly. Then, they are superimposed to form the spectral function. Finally, the Green's function is reconstructed from the spectral function via the Laplace transformation. This procedure allows for the generation of lots of spectral functions and corresponding Green's functions, creating datasets for testing analytic continuation methods and codes.