Digitising SU(2) Gauge Fields and the Freezing Transition

TL;DR

This paper analyzes the freezing transition in discretized SU(2) gauge fields, proposing a subset selection method that enables unfrozen Monte Carlo simulations across all couplings, with a focus on efficient subset constructions like the Fibonacci spiral.

Contribution

It provides a comprehensive analysis of freezing phenomena in SU(2) discretizations and introduces an efficient subset construction method to avoid freezing in simulations.

Findings

Appropriate subset choices prevent freezing at all couplings.

Uneven point weights require careful handling.

Fibonacci spiral subsets are near optimal.

Abstract

Efficient discretisations of gauge groups are crucial with the long term perspective of using tensor networks or quantum computers for lattice gauge theory simulations. For any Lie group other than U$(1)$, however, there is no class of asymptotically dense discrete subgroups. Therefore, discretisations limited to subgroups are bound to lead to a freezing of Monte Carlo simulations at weak couplings, necessitating alternative partitionings without a group structure. In this work we provide a comprehensive analysis of this freezing for all discrete subgroups of SU$(2)$ and different classes of asymptotically dense subsets. We find that an appropriate choice of the subset allows unfrozen simulations for arbitrary couplings, though one has to be careful with varying weights of unevenly distributed points. A generalised version of the Fibonacci spiral appears to be particularly efficient and close to optimal.