Digitising SU(2) gauge fields and the freezing transition

Tobias Hartung, Timo Jakobs, Karl Jansen, Johann Ostmeyer, Carsten Urbach

Research output: Contribution to journalArticlepeer-review

18 Citations (SciVal)

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.

Original languageEnglish
Article number237
JournalEuropean Physical Journal C
Volume82
Issue number3
DOIs
Publication statusPublished - 20 Mar 2022

Bibliographical note

Funding Information:
This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) and the NSFC through the funds provided to the Sino-German Collaborative Research Center CRC 110 “Symmetries and the Emergence of Structure in QCD” (DFG Project-ID 196253076 - TRR 110, NSFC Grant No. 12070131001) as well as the STFC Consolidated Grant ST/T000988/1. The open source software packages R [] and hadron [] have been used.

Funding Information:
This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) and the NSFC through the funds provided to the Sino-German Collaborative Research Center CRC 110 ?Symmetries and the Emergence of Structure in QCD? (DFG Project-ID 196253076 - TRR 110, NSFC Grant No.?12070131001) as well as the STFC Consolidated Grant ST/T000988/1. The open source software packages R [31] and hadron [29] have been used.

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Physics and Astronomy (miscellaneous)

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