Normalizing-flow-based density of states for (1+1)D U(1) lattice gauge theory with a $\theta$-term

TL;DR

This paper extends the normalizing-flow-based density-of-states method to (1+1)D U(1) lattice gauge theory, successfully reproducing known results and enabling fixed-topology configuration generation with a $ heta$-term.

Contribution

It introduces gauge-equivariant normalizing flows for lattice gauge theories, expanding the density-of-states approach to gauge fields with topological terms.

Findings

Reproduces analytic results for pure gauge theory without $ heta$-term

Enables generation of configurations at fixed topological charge with $ heta$-term

Validates the method's applicability to gauge theories with topological features

Abstract

A normalizing-flow-based implementation of the density-of-states approach has recently been used to successfully reconstruct the partition function of (1+1)D scalar lattice field theory. In this preliminary work, we extend this framework to a lattice gauge theory by employing gauge-equivariant normalizing flows to reconstruct the density of states of pure (1+1)D U(1) lattice gauge theory, both with and without a $\theta$-term. In the absence of a $\theta$-term, we first demonstrate that the normalizing-flow-based reconstruction of the density of states reproduces the known analytic results for this theory. We further show that, in the presence of a $\theta$-term, this formulation enables the generation of gauge-field configurations at fixed values of the topological charge.