Digitising SU(2) gauge fields and the freezing transition

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

doi:10.1140/epjc/s10052-022-10192-5

Digitising SU(2) gauge fields and the freezing transition

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

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

23 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 language	English
Article number	237
Journal	European Physical Journal C
Volume	82
Issue number	3
DOIs	https://doi.org/10.1140/epjc/s10052-022-10192-5
Publication status	Published - 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.

Funding

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. 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)

Access to Document

10.1140/epjc/s10052-022-10192-5Licence: CC BY

Cite this

@article{3c72849f92554d5792ebade8741cadc4,

title = "Digitising SU(2) gauge fields and the freezing transition",

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.",

author = "Tobias Hartung and Timo Jakobs and Karl Jansen and Johann Ostmeyer and Carsten Urbach",

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. ",

year = "2022",

month = mar,

day = "20",

doi = "10.1140/epjc/s10052-022-10192-5",

language = "English",

volume = "82",

journal = "European Physical Journal C",

issn = "1434-6044",

publisher = "Springer Nature",

number = "3",

}

TY - JOUR

T1 - Digitising SU(2) gauge fields and the freezing transition

AU - Hartung, Tobias

AU - Jakobs, Timo

AU - Jansen, Karl

AU - Ostmeyer, Johann

AU - Urbach, Carsten

N1 - 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.

PY - 2022/3/20

Y1 - 2022/3/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85126818955&partnerID=8YFLogxK

U2 - 10.1140/epjc/s10052-022-10192-5

DO - 10.1140/epjc/s10052-022-10192-5

M3 - Article

AN - SCOPUS:85126818955

SN - 1434-6044

VL - 82

JO - European Physical Journal C

JF - European Physical Journal C

IS - 3

M1 - 237

ER -

Digitising SU(2) gauge fields and the freezing transition

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this