Locality-constrained autoregressive cum conditional normalizing flow for lattice field theory simulations

TL;DR

This paper introduces a locality-constrained autoregressive normalizing flow model for lattice field theory simulations, significantly improving sampling efficiency and reducing autocorrelation times compared to traditional models.

Contribution

It proposes the local-Autoregressive Conditional Normalizing Flow (l-ACNF) that leverages locality to simplify input domains and enhance sampling performance in lattice quantum field theories.

Findings

l-ACNF outperforms full-lattice normalizing flows in autocorrelation times

Model efficiently samples ^{4} theory on 2D lattices

Autocorrelation times are reduced by orders of magnitude

Abstract

Normalizing flow-based sampling methods have been successful in tackling computational challenges traditionally associated with simulating lattice quantum field theories. Further works have incorporated gauge and translational invariance of the action integral in the underlying neural networks, which have led to efficient training and inference in those models. In this paper, we incorporate locality of the action integral which leads to simplifications to the input domain of conditional normalizing flows that sample constant time sub-lattices in an autoregressive process, dubbed local-Autoregressive Conditional Normalizing Flow (l-ACNF). We find that the autocorrelation times of l-ACNF models outperform an equivalent normalizing flow model on the full lattice by orders of magnitude when sampling $\phi^{4}$ theory on a 2 dimensional lattice.