ACFlow: An open source toolkit for analytical continuation of quantum Monte Carlo data

Abstract

The purpose of analytical continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, and dynamical susceptibilities) from noisy data generated in finite temperature quantum Monte Carlo simulations. It requires numerical solutions of a family of Fredholm integral equations of the first kind, which is indeed a challenging task. In this paper, an open source toolkit (dubbed ACFlow) for analytical continuation of quantum Monte Carlo data is presented. We at first give a short introduction to the analytical continuation problem. Next, three primary analytical continuation algorithms, including maximum entropy method, stochastic analytical continuation, and stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate major features, implementation details, and basic usage of this toolkit. Finally, four representative examples are shown to demonstrate usefulness and flexibility of the ACFlow toolkit.

arXiv comment26 pages, 7 figures

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• Estimates of the dynamic structure factor for the finite temperature electron liquid via analytic continuation of path integral Monte Carlo data
• Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Classical dynamics of the antiferromagnetic Heisenberg $S=1/2$ spin ladder
• SmoQyDEAC.jl: A differential evolution package for the analytic continuation of imaginary time correlation functions
• Supersolid Phase in the Diluted Holstein Model
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language
• The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem
• Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism
• PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods