Neural Network Analytic Continuation for Monte Carlo: Improvement by Statistical Errors

TL;DR

This paper presents a neural network approach for analytic continuation of Monte Carlo data, emphasizing the importance of matching statistical error properties in training data, and demonstrates superior performance over traditional methods in noisy scenarios.

Contribution

We developed a systematic method to synthesize training datasets with realistic noise properties, enhancing neural network performance for spectral extraction from Monte Carlo data.

Findings

Neural network method outperforms maximum entropy in noisy conditions.

Matching training data noise properties improves spectral reconstruction.

Successfully applied to quantum Monte Carlo data of spin chains.

Abstract

This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are carefully synthesized without ``data leakage". We found that the training set should match the input correlation functions in terms of statistical error properties, such as noise level, noise dependence on imaginary time, and imaginary time-displaced correlations. We have developed a systematic method to synthesize such training datasets. Our improved algorithm outperform the widely used maximum entropy method in highly noisy situations. As an example, our method successfully extracted the dynamic structure factor of the spin-1/2 Heisenberg chain from quantum Monte Carlo simulations.