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

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

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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.
Subject	Physics
Related Publication	Is Supplement To: 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)arXiv: 2503.11480v1
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Persistent Identifier	doi:10.60507/FK2/AUJJ08
Publication Date	2025-08-20
Title	Code and scripts for ``Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory''
Author	Groß, Christiane Franziska (Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität Bonn) - ORCID: https://orcid.org/0009-0009-5876-1455 Romiti, Simone (Institute for Theoretical Physics, Albert Einstein Center for Fundamental Physics, University of Bern) - ORCID: https://orcid.org/0000-0002-6509-447X Funcke, Lena (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) - ORCID: https://orcid.org/0000-0001-5022-9506 Jansen, Karl (Computation-Based Science and Technology Research Center, The Cyprus Institute and Deutsches Elektronen-Synchrotron DESY) - ORCID: https://orcid.org/0000-0002-1574-7591 Kan, Angus (Institute for Quantum Computing and Department of Physics & Astronomy, University of Waterloo) - ORCID: https://orcid.org/0000-0002-5699-365X Kühn, Stefan (Deutsches Elektronen-Synchrotron DESY) - ORCID: https://orcid.org/0000-0001-7693-350X Urbach, Carsten (Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität Bonn) - ORCID: https://orcid.org/0000-0003-1412-7582
Point of Contact	Use email button above to contact. Groß, Christiane Franziska (University of Bonn)
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.
Subject	Physics
Subject Refinement	hep-lat quant-ph
Keyword	hep-lat quant-ph Hamiltonian Lattice Gauge Theory Anisotropic Lattice Pure Gauge Theory U(1) Gauge Theory Numerical Simulation
Related Publication	Is Supplement To: 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) arXiv 2503.11480v1 https://arxiv.org/abs/2503.11480v1
Funding Information	Deutsche Forschungsgemeinschaft: CRC 1639 NuMeriQS – project no. 511713970 MKW NRW: NRW-FAIR, funding code NW21-024-A Ministry of Science, Research and Culture of the State of Brandenburg: Center for Quantum Technology and Applications (CQTA) European Union’s Horizon Europe Framework Programme (HORIZON) under the ERA Chair scheme: grant agreement no. 101087126
Depositor	Groß, Christiane
Deposit Date	2025-08-11
Date of Collection	Start Date: 2022-01 ; End Date: 2025-03
Software	R, Version: 4.1.2 C++, Version: C++17

Computational Workflow Metadata

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

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