https://doi.org/10.1140/epjc/s10052-022-10192-5
Regular Article - Theoretical Physics
Digitising SU(2) gauge fields and the freezing transition
1
Department of Mathematical Sciences, University of Bath, 4 West, Claverton Down, BA2 7AY, Bath, UK
2
Computation-Based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Street, 2121, Nicosia, Cyprus
3
Helmholtz-Institut für Strahlen- und Kernphysik, University of Bonn, Nussallee 14-16, 53115, Bonn, Germany
4
Bethe Center for Theoretical Physics, University of Bonn, Nussallee 12, 53115, Bonn, Germany
5
NIC, DESY Zeuthen, Platanenallee 6, 15738, Zeuthen, Germany
6
Department of Mathematical Sciences, University of Liverpool, L69 7ZL, Liverpool, UK
Received:
31
January
2022
Accepted:
7
March
2022
Published online:
20
March
2022
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.
© The Author(s) 2022
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
