Sampling using $SU(N)$ gauge equivariant flows
This work addresses sampling challenges in lattice gauge theories for physics researchers, presenting a novel method for a known bottleneck.
The paper tackled the problem of sampling in SU(N) lattice gauge theories by developing a gauge-invariant flow-based algorithm, resulting in a method that respects matrix conjugation symmetry and was applied to sample distributions for SU(2) and SU(3) in two dimensions.
We develop a flow-based sampling algorithm for $SU(N)$ lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an $SU(N)$ variable (or on a $U(N)$ variable by a simple alternative) that respect matrix conjugation symmetry. We apply this technique to sample distributions of single $SU(N)$ variables and to construct flow-based samplers for $SU(2)$ and $SU(3)$ lattice gauge theory in two dimensions.