{"title":"Generalized HMC using Nambu mechanics for lattice QCD","authors":"Erik Lundstrum","doi":"10.1103/physrevd.111.034512","DOIUrl":null,"url":null,"abstract":"We describe a generalization of the hybrid Monte Carlo (HMC) algorithm in which the molecular dynamics steps utilize Nambu generalized Hamiltonian dynamics. Nambu mechanics contains multiple Hamiltonian functions. Using one of these Hamiltonians in the Metropolis accept/reject step is enough to guarantee the correct target distribution. The other Hamiltonians can include arbitrary functions of the gauge field. We examine the simplest case with two Hamiltonians and choose the second to include nonlocal functions of the gauge field. In this way, the links are updated with instantaneous knowledge of far-separated link variables. This represents a promising method for reducing critical slowing down in lattice QCD simulations. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"347 1","pages":""},"PeriodicalIF":5.3000,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.034512","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
Abstract
We describe a generalization of the hybrid Monte Carlo (HMC) algorithm in which the molecular dynamics steps utilize Nambu generalized Hamiltonian dynamics. Nambu mechanics contains multiple Hamiltonian functions. Using one of these Hamiltonians in the Metropolis accept/reject step is enough to guarantee the correct target distribution. The other Hamiltonians can include arbitrary functions of the gauge field. We examine the simplest case with two Hamiltonians and choose the second to include nonlocal functions of the gauge field. In this way, the links are updated with instantaneous knowledge of far-separated link variables. This represents a promising method for reducing critical slowing down in lattice QCD simulations. Published by the American Physical Society2025
期刊介绍：
Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics.
PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including:
Particle physics experiments,
Electroweak interactions,
Strong interactions,
Lattice field theories, lattice QCD,
Beyond the standard model physics,
Phenomenological aspects of field theory, general methods,
Gravity, cosmology, cosmic rays,
Astrophysics and astroparticle physics,
General relativity,
Formal aspects of field theory, field theory in curved space,
String theory, quantum gravity, gauge/gravity duality.
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