Fast and Efficient Stochastic Optimization for Analytic Continuation

TL;DR

This paper introduces FESOM, a fast stochastic optimization method for analytic continuation of quantum Monte Carlo data, which performs comparably to Maximum Entropy and better resolves fine structures in poor-quality data.

Contribution

FESOM offers a more accessible, efficient stochastic approach for analytic continuation, providing detailed uncertainty estimates and improved resolution for low-quality data.

Findings

FESOM yields spectra similar to Maximum Entropy for high-quality data.

FESOM resolves fine spectral structures better with poor-quality data.

FESOM provides detailed frequency-dependent uncertainty information.

Abstract

The analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM) as a more accessible variant of the stochastic optimization method introduced by Mishchenko et al. and benchmark the resulting spectra with those obtained by the standard Maximum Entropy method for three representative test cases, in- cluding data taken from studies of the two-dimensional Hubbard model. We generally find that our FESOM approach gives spectra similar to the Maximum Entropy results. In particular, while the Maximum Entropy method gives superior results when the quality of the data is strong, we find that FESOM is able to resolve fine structure with more detail when the quality of the data is poor. In addition, because of its stochastic nature, the method provides detailed information on the frequency dependent uncertainty of the resulting spectra, while the Maximum Entropy method does so only for the spectral weight integrated over a finite frequency region. We therefore believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used Maximum Entropy method especially for data with poor quality.