A Parameter-Free Differential Evolution Algorithm for the Analytic Continuation of Imaginary Time Correlation Functions

TL;DR

This paper introduces DEAC, a parameter-free evolutionary algorithm that efficiently performs analytic continuation of imaginary time correlation functions, improving spectral accuracy with less computational effort.

Contribution

The paper presents a novel parameter-free differential evolution algorithm that automates parameter tuning, enhancing spectral fidelity in quantum many-body physics applications.

Findings

Achieves higher spectral fidelity in less CPU time.

Successfully applied to quantum Monte Carlo data of bulk helium.

Demonstrates robustness without manual parameter tuning.

Abstract

We report on Differential Evolution for Analytic Continuation (DEAC): a parameter-free evolutionary algorithm to generate the dynamic structure factor from imaginary time correlation functions. Our approach to this long-standing problem in quantum many-body physics achieves enhanced spectral fidelity while using fewer compute (CPU) hours. The need for fine-tuning of algorithmic control parameters is eliminated by embedding them within the genome to be optimized for this evolutionary computation based algorithm. Benchmarks are presented for models where the dynamic structure factor is known exactly, and experimentally relevant results are included for quantum Monte Carlo simulations of bulk $^4$He below the superfluid transition temperature.