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Lattice field theory

Section status

Contributor: Unclaimed — this section has no named author yet. See Contribute.

Last reviewed: —

Status: Stub — a starting point only. The curated list is not yet written.

Overview

The cost of sampling gauge configurations limits lattice calculations. Markov chain Monte Carlo suffers critical slowing down near the continuum limit: autocorrelation times grow, and topological sectors become effectively disconnected, so more computing buys progressively less independent data. Flow-based sampling is the most developed response. A normalizing flow is trained to map a simple distribution to the target gauge measure and, combined with an accept/reject step, gives asymptotically exact sampling rather than an approximation. Gauge symmetry must be built into the architecture, so this section and equivariant architectures are two views of similar work.

  • Lecture Notes on Normalizing Flows for Lattice Quantum Field Theories, Cheng et al. (2025) (arXiv:2504.18126) — lecture notes on normalizing flows for lattice quantum field theories
  • Machine-learning approaches to accelerating lattice simulations, Lawrence (2025) (arXiv:2502.02670) — a review of ML approaches to accelerating lattice simulations
  • Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning, Shanahan et al. (2022) (arXiv:2209.07559) — the Snowmass computational-frontier report, for where this sits in the field's computing plans

Curated paper list

This list is a seed, not a curated selection

A few landmark papers are listed to give the section a starting shape. A proper curated list — thematically grouped, with an annotation on every entry — is what this section still needs. See Contribute.

  • Flow-based generative models for Markov chain Monte Carlo in lattice field theory, Albergo et al. (2019) (arXiv:1904.12072) — introduced flow-based generative models for lattice field theory, in a scalar theory
  • Equivariant flow-based sampling for lattice gauge theory, Kanwar et al. (2020) (arXiv:2003.06413) — extended this to gauge fields with the required equivariance — the foundational result for the area
  • Reducing Autocorrelation Times in Lattice Simulations with Generative Adversarial Networks, Urban et al. (2018) (arXiv:1811.03533) — an earlier adversarial attempt at reducing autocorrelation times, useful as contrast

Benchmarks, datasets & software

Not yet compiled for this section.

Open questions

What is settled here, what is contested, and what remains unsolved? This is the part a bibliography structurally cannot provide, and often the most useful paragraph on the page.

Further reading

Relevant work that is not an entry point — too specialized, too recent, or simply not where a newcomer should start. Suggestions that do not fit the curated list above belong here rather than being turned away.

Nothing listed yet.

Cross-references