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

• DOI: 10.48550/arxiv.2302.11317
• Publication Date: 2023-06-01
• Authors: Sun, Kai-Wei; Wang, Fa
• Keywords: 0103 physical sciences; FOS: Physical sciences; Disordered Systems and Neural Networks (cond-mat.dis-nn); Condensed Matter - Disordered Systems and Neural Networks; 01 natural sciences

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 find 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 outperforms 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.