Flow-based sampling for fermionic lattice field theories

2021/06/30 by Michael S. Albergo, Gurtej Kanwar, Sébastien Racanière +8 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Fermion #Gauge theory #Geometry #Lattice (music) #Lattice field theory #Lattice gauge theory #Markov Chains and Monte Carlo Methods #Massless particle #Mathematics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scalar (mathematics) #Scalar field #Statistical physics #Stochastic processes and statistical mechanics #Theoretical physics #cond-mat.stat-mech #cs.LG #hep-lat

paper · pdf · doi:10.1103/physrevd.104.114507

published in Physical review. D/Physical review. D. 104(11) (American Physical Society) · 26 pages, 5 figures

openalex publication_date 2021/12/15 · arxiv created 2021/12/28 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction.

Citations

• Exact pseudofermion action for Monte Carlo simulation of domain-wall fermion
• On Information and Sufficiency
• UV-filtered fermionic Monte Carlo
• Duality in field theory and statistical systems
• Equation of State Calculations by Fast Computing Machines
• Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
• Recent Developments of World-Line Monte Carlo Methods
• The pseudo-marginal approach for efficient Monte Carlo computations
• Trivializing maps, the Wilson flow and the HMC algorithm
• Schwarz-preconditioned HMC algorithm for two-flavor lattice QCD
• Monte Carlo sampling methods using Markov chains and their applications
• Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions
• Hamiltonian formulation of Wilson's lattice gauge theories
• A high-bias, low-variance introduction to Machine Learning for physicists
• Lattice Gauge Theories
• Equivariant Flow-Based Sampling for Lattice Gauge Theory
• Machine learning for quantum matter
• Generative neural samplers for the quantum Heisenberg chain
• The Generalization of Student's Ratio