Overcoming Ergodicity Problems of the Hybrid Monte Carlo Method using Radial Updates

Fuente: arXiv
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Main Authors: Temmen, Finn, Berkowitz, Evan, Kennedy, Anthony, Luu, Thomas, Ostmeyer, Johann, Yu, Xinhao
Format: Preprint
Published: 2024
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author Temmen, Finn
Berkowitz, Evan
Kennedy, Anthony
Luu, Thomas
Ostmeyer, Johann
Yu, Xinhao
author_facet Temmen, Finn
Berkowitz, Evan
Kennedy, Anthony
Luu, Thomas
Ostmeyer, Johann
Yu, Xinhao
contents Despite its many advantages, the sensible application of the Hybrid Monte Carlo (HMC) method is often hindered by the presence of large - or even infinite - potential barriers. These potential barriers partition the configuration space into distinct sectors, which leads to ergodicity violations and biased measurements of observables. In this work, we address this problem by augmenting the HMC method with a multiplicative Metropolis-Hastings update in a so-called "radial direction" of the fields, which enables jumps over the aforementioned potential barriers at comparably low computational cost. The effectiveness of this approach is demonstrated for the Hubbard model, formulated in a non-compact space by means of a continuous Hubbard-Stratonovich transformation. Our numerical results show that the radial updates successfully resolve the ergodicity violation, while simultaneously reducing autocorrelations.
format Preprint
id arxiv_https___arxiv_org_abs_2410_19148
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Overcoming Ergodicity Problems of the Hybrid Monte Carlo Method using Radial Updates
Temmen, Finn
Berkowitz, Evan
Kennedy, Anthony
Luu, Thomas
Ostmeyer, Johann
Yu, Xinhao
Strongly Correlated Electrons
Despite its many advantages, the sensible application of the Hybrid Monte Carlo (HMC) method is often hindered by the presence of large - or even infinite - potential barriers. These potential barriers partition the configuration space into distinct sectors, which leads to ergodicity violations and biased measurements of observables. In this work, we address this problem by augmenting the HMC method with a multiplicative Metropolis-Hastings update in a so-called "radial direction" of the fields, which enables jumps over the aforementioned potential barriers at comparably low computational cost. The effectiveness of this approach is demonstrated for the Hubbard model, formulated in a non-compact space by means of a continuous Hubbard-Stratonovich transformation. Our numerical results show that the radial updates successfully resolve the ergodicity violation, while simultaneously reducing autocorrelations.
title Overcoming Ergodicity Problems of the Hybrid Monte Carlo Method using Radial Updates
topic Strongly Correlated Electrons
url https://arxiv.org/abs/2410.19148