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, spin and charge 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 popular analytical continuation algorithms, including the maximum entropy method, the stochastic analytical continuation, and the stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate major features, implementation details, basic usage, inputs and outputs of this toolkit. Finally, four representative examples, including analytical continuations of Matsubara self-energy function, Matsubara and imaginary time Green's functions, and current-current correlation function, are shown to demonstrate usefulness and flexibility of the ACFlow toolkit.

Locations

• arXiv (Cornell University) - View - PDF