Smoothing and extrapolating shifted-contour auxiliary-field Monte Carlo signals using discrete Laguerre functions

TL;DR

This paper introduces a novel smoothing and extrapolation method using discrete Laguerre functions for analyzing stochastic signals in shifted-contour auxiliary-field Monte Carlo, balancing stability and accuracy.

Contribution

It presents a new systematic approach for signal analysis in Monte Carlo simulations, including a heuristic algorithm for optimal parameter selection.

Findings

Low order N provides stability for small iteration signals.

Higher order N improves extrapolation accuracy for large iteration signals.

The method effectively reduces errors in Monte Carlo energy estimates.

Abstract

We develop a new smoothing or extrapolating method, based on discrete Laguerre functions, for systematically analyzing the stochastic signal of shifted-contour auxiliary-field Monte Carlo. We study the statistical errors and extrapolation errors using full configuration-interaction energies for the doubly stretched water molecule. The only free parameter is the order N of the fit. We show that low N emphasizes stability while higher N enable improved extrapolation, at the cost of increased statistical errors. Typically, one should use low order for signals based on a small number of iterations while higher order is efficacious for signals based on large number of iterations. We provide a heuristic algorithm for determining the order to be used and show its utility.