Cross Validation in Stochastic Analytic Continuation
Abstract
Stochastic Analytic Continuation (SAC) of Quantum Monte Carlo (QMC) imaginary-time correlation function data is a valuable tool in connecting many-body models to experimentally measurable dynamic response functions. Recent developments of the SAC method have allowed for spectral functions with sharp features, e.g. narrow peaks and divergent edges, to be resolved with unprecedented fidelity. Often times, it is not known what exact sharp features, if any, are present extit{a priori}, and, due to the ill-posed nature of the analytic continuation problem, multiple spectral representations may be acceptable. In this work, we borrow from the machine learning and statistics literature and implement a cross validation technique to provide an unbiased method to identify the most likely spectrum amongst a set obtained with different spectral parameterizations and imposed constraints. We demonstrate the power of this method with examples using imaginary-time data generated by QMC simulations and synthetic data generated from artificial spectra. Our procedure, which can be considered a form of model selection, can be applied to a variety of numerical analytic continuation methods, beyond just SAC.
AI-Generated Overview
Here is a brief overview of the provided text from the scientific paper, organized under the requested bullet points:
-
Research Focus: The study explores the implementation of cross-validation techniques in Stochastic Analytic Continuation (SAC) methods, aiming to improve the identification of the most likely spectral representation from quantum Monte Carlo (QMC) generated data.
-
Methodology: The authors utilize a cross-validation procedure wherein a dataset of imaginary-time correlation functions is partitioned into training and validation sets. The goodness-of-fit is assessed using the χ² statistic, and different spectral parameterizations are compared.
-
Results: The findings demonstrate that cross-validation enhances the predictive power of SAC by effectively identifying optimal sampling temperatures and parameterizations, particularly in cases with complex spectral features.
-
Key Contribution(s): The key contributions of this work include the advancement of cross-validation as a method for model selection in analytic continuation, providing a systematic way to discriminate between spectral models based on their fit to QMC-generated data.
-
Significance: This approach holds significance in the field of quantum many-body physics, as it addresses the inherent challenges of extracting information from numerical simulations and improves the reliability of analytic continuation methods.
-
Broader Applications: The proposed cross-validation method can extend beyond SAC to other analytic continuation techniques, such as the Maximum Entropy Method (MEM), facilitating better resolution of spectral features in various physical systems and models.