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Code and scripts for ``Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory''

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Important usage condition: Use and redistribution are governed by License not specified. Review and comply with the license before using the data.
Persistent identifier
doi:10.60507/FK2/AUJJ08
Published version
1.0
Publication date
2025-08-20
License
License not specified

Important: custom terms of use

The files in the folders "code" and "analysis" are licensed under the GNU general public license version 3.0(https://www.gnu.org/licenses/gpl-3.0.html). The files in the folders "how_to_install" and "scripts" are licensed under the license CC BY 4.0(https://creativecommons.org/licenses/by/4.0/). A copy of the respective license is contained in each folder.

Description

At finite lattice spacing, Lagrangian and Hamiltonian predictions differ due to discretization effects. In the Hamiltonian limit, i.e. at vanishing temporal lattice spacing a_t, the path integral approach in the Lagrangian formalism reproduces the results of the Hamiltonian theory. In this work, we numerically calculate the Hamiltonian limit of a U(1) gauge theory in (2+1) dimensions. This is achieved by Monte Carlo simulations in the Lagrangian formalism with lattices that are anisotropic in the time direction. For each ensemble, we determine the ratio between the temporal and spatial scale with the static quark potential and extrapolate to a_t to 0. Our results are compared with the data from Hamiltonian simulations at small volumes, showing agreement within <2 sigma. These results can be used to match the two formalisms. Here we provide the code and scripts needed to reproduce our results.

Creators

Keywords

hep-lat, quant-ph, Hamiltonian Lattice Gauge Theory, Anisotropic Lattice, Pure Gauge Theory, U(1) Gauge Theory, Numerical Simulation

Files

Before downloading: Use and redistribution are governed by License not specified. Review and comply with the license before using the data.
FileTypeBytesChecksum
data.zipapplication/zip263910MD5 9c1052c22417070b3c96a2ac30007058
README.txttext/plain12306MD5 2f7acb8689c8e4881c0fd0dba5a35763

Citation

Groß, Christiane Franziska; Romiti, Simone; Funcke, Lena; Jansen, Karl; Kan, Angus; Kühn, Stefan; Urbach, Carsten, 2025-08-20, Code and scripts for ``Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory'', doi:10.60507/FK2/AUJJ08, V1.0

Additional Dataverse fields

Id467
Dataset Typedataset
Internal Version Number33
Latest Version Publishing StateRELEASED
Release Time2025-08-20T13:56:41Z
Create Time2025-08-11T17:02:02Z
Citation Date2025-08-20
File Access RequestTrue

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Citation Metadata

Title title
Code and scripts for ``Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory''
Author author
  1. Author Name
    Groß, Christiane Franziska
    Author Affiliation
    Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität Bonn
    Author Identifier Scheme
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    Type Class
    primitive
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    https://orcid.org/0009-0009-5876-1455
    Expandedvalue
    Person Name
    Groß, Christiane Franziska
    @id
    https://orcid.org/0009-0009-5876-1455
    Scheme
    ORCID
    @type
    https://schema.org/Person
  2. Author Name
    Romiti, Simone
    Author Affiliation
    Institute for Theoretical Physics, Albert Einstein Center for Fundamental Physics, University of Bern
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
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    https://orcid.org/0000-0002-6509-447X
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    Person Name
    Romiti, Simone
    @id
    https://orcid.org/0000-0002-6509-447X
    Scheme
    ORCID
    @type
    https://schema.org/Person
  3. Author Name
    Funcke, Lena
    Author Affiliation
    Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität Bonn and Transdisciplinary Research Area ``Building Blocks of Matter and Fundamental Interactions'' (TRA Matter), Rheinische Friedrich-Wilhelms-Universität Bonn
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
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    False
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    primitive
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    https://orcid.org/0000-0001-5022-9506
    Expandedvalue
    Person Name
    Funcke, Lena
    @id
    https://orcid.org/0000-0001-5022-9506
    Scheme
    ORCID
    @type
    https://schema.org/Person
  4. Author Name
    Jansen, Karl
    Author Affiliation
    Computation-Based Science and Technology Research Center, The Cyprus Institute and Deutsches Elektronen-Synchrotron DESY
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
    primitive
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    https://orcid.org/0000-0002-1574-7591
    Expandedvalue
    Person Name
    Jansen, Karl
    @id
    https://orcid.org/0000-0002-1574-7591
    Scheme
    ORCID
    @type
    https://schema.org/Person
  5. Author Name
    Kan, Angus
    Author Affiliation
    Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
    primitive
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    https://orcid.org/0000-0002-5699-365X
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    Person Name
    Kan, Angus
    @id
    https://orcid.org/0000-0002-5699-365X
    Scheme
    ORCID
    @type
    https://schema.org/Person
  6. Author Name
    Kühn, Stefan
    Author Affiliation
    Deutsches Elektronen-Synchrotron DESY
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
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    Multiple
    False
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    Person Name
    Kühn, Stefan
    @id
    https://orcid.org/0000-0001-7693-350X
    Scheme
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  7. Author Name
    Urbach, Carsten
    Author Affiliation
    Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität Bonn
    Author Identifier Scheme
    ORCID
    Author Identifier
    Type Name
    authorIdentifier
    Multiple
    False
    Type Class
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    https://orcid.org/0000-0003-1412-7582
    Expandedvalue
    Person Name
    Urbach, Carsten
    @id
    https://orcid.org/0000-0003-1412-7582
    Scheme
    ORCID
    @type
    https://schema.org/Person
Dataset Contact datasetContact
  1. Dataset Contact Name
    Groß, Christiane Franziska
    Dataset Contact Affiliation
    University of Bonn
    Dataset Contact Email
    s6chgros@uni-bonn.de
Ds Description dsDescription
  1. Ds Description Value
    At finite lattice spacing, Lagrangian and Hamiltonian predictions differ due to discretization effects. In the Hamiltonian limit, i.e. at vanishing temporal lattice spacing a_t, the path integral approach in the Lagrangian formalism reproduces the results of the Hamiltonian theory. In this work, we numerically calculate the Hamiltonian limit of a U(1) gauge theory in (2+1) dimensions. This is achieved by Monte Carlo simulations in the Lagrangian formalism with lattices that are anisotropic in the time direction. For each ensemble, we determine the ratio between the temporal and spatial scale with the static quark potential and extrapolate to a_t to 0. Our results are compared with the data from Hamiltonian simulations at small volumes, showing agreement within <2 sigma. These results can be used to match the two formalisms. Here we provide the code and scripts needed to reproduce our results.
Subject subject
  1. Physics
Subject Refinement subjectRefinement
  1. Subject Refinement Value
    hep-lat
  2. Subject Refinement Value
    quant-ph
Free Keyword freeKeyword
  1. Free Keyword Value
    hep-lat
  2. Free Keyword Value
    quant-ph
  3. Free Keyword Value
    Hamiltonian Lattice Gauge Theory
  4. Free Keyword Value
    Anisotropic Lattice
  5. Free Keyword Value
    Pure Gauge Theory
  6. Free Keyword Value
    U(1) Gauge Theory
  7. Free Keyword Value
    Numerical Simulation
Publication publication
  1. Publication Relation Type
    IsSupplementTo
    Publication Citation
    Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory - C.F. Groß (Bonn U., HISKP and U. Bonn, Phys. Inst., BCTP), S. Romiti (Bern U. and U. Bern, AEC), L. Funcke (Bonn U., HISKP and U. Bonn, Phys. Inst., BCTP), K. Jansen (Cyprus Inst. and DESY, Zeuthen), A. Kan (Waterloo U.), S. Kühn (DESY, Zeuthen) and C. Urbach(Bonn U., HISKP and U. Bonn, Phys. Inst., BCTP)
    Publication IDType
    arXiv
    Publication IDNumber
    2503.11480v1
    Publication URL
    https://arxiv.org/abs/2503.11480v1
Grant Number grantNumber
  1. Grant Number Agency
    Deutsche Forschungsgemeinschaft
    Grant Number Value
    CRC 1639 NuMeriQS – project no. 511713970
  2. Grant Number Agency
    MKW NRW
    Grant Number Value
    NRW-FAIR, funding code NW21-024-A
  3. Grant Number Agency
    Ministry of Science, Research and Culture of the State of Brandenburg
    Grant Number Value
    Center for Quantum Technology and Applications (CQTA)
  4. Grant Number Agency
    European Union’s Horizon Europe Framework Programme (HORIZON) under the ERA Chair scheme
    Grant Number Value
    grant agreement no. 101087126
Depositor depositor
Groß, Christiane
Date Of Deposit dateOfDeposit
2025-08-11
Date Of Collection dateOfCollection
  1. Date Of Collection Start
    2022-01
    Date Of Collection End
    2025-03
Software software
  1. Software Name
    R
    Software Version
    4.1.2
  2. Software Name
    C++
    Software Version
    C++17

Computational Workflow Metadata

Workflow Type workflowType
  1. Other
Workflow Code Repository workflowCodeRepository
  1. https://github.com/christianegross/U1_analyse_potential/tree/clean_for_publication
  2. https://github.com/HISKP-LQCD/su2/tree/su3
Workflow Documentation workflowDocumentation
  1. See the file README.md in the folder scripts for a detailed description of the workflow.

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