Implementation of the maximum entropy method for analytic continuation

Abstract

We present Maxent, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to the real axis. The code works for imaginary time and Matsubara frequency data and implements the ‘Legendre’ representation of finite temperature Green’s functions. It implements a variety of kernels, default models, and grids for continuing bosonic, fermionic, anomalous, and other data. Our implementation is licensed under GPLv3 and extensively documented. This paper shows the use of the programs in detail. Program summaryProgram Title: maxentProgram Filesdoi:http://dx.doi.org/10.17632/rf3p4psdhs.1Licensing provisions: GPLv3Programming language: C++Nature of problem: The analytic continuation of imaginary axis correlation functions to real frequency/time variables is an ill-posed problem which has an infinite number of solutions.Solution method: The maximum entropy method obtains a possible solution that maximizes entropy, enforces sum rules, and otherwise produces ‘smooth’ curves. Our implementation allows for input in Matsubara frequencies, imaginary time, or a Legendre expansion. It implements a range of bosonic, fermionic and generalized kernels for normal and anomalous Green’s functions, self-energies, and two-particle response functions.External routines/libraries: ALPSCore [1][2], GSL, HDF5 [1]B. Bauer, et al., The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. Theor. Exp. 2011 (05) (2011) P05001. arXiv:1101.2646, doi:10.1088/17425468/2011/ 05/P05001.[2]A. Gaenko, E. Gull, A.E. Antipov, L. Gamper, G. Carcassi, J. Paki, R. Levy, M. Dolfi, J. Greitemann, J.P.F. LeBlanc, Alpscore: Version 0.5.4doi: 10.5281/zenodo.50203.