10.60507/FK2/AUJJ08Groß, Christiane FranziskaChristiane FranziskaGroß0009-0009-5876-1455Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität BonnRomiti, SimoneSimoneRomiti0000-0002-6509-447XInstitute for Theoretical Physics, Albert Einstein Center for Fundamental Physics, University of BernFuncke, LenaLenaFuncke0000-0001-5022-9506Helmholtz 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 BonnJansen, KarlKarlJansen0000-0002-1574-7591Computation-Based Science and Technology Research Center, The Cyprus Institute and Deutsches Elektronen-Synchrotron DESYKan, AngusAngusKan0000-0002-5699-365XInstitute for Quantum Computing and Department of Physics & Astronomy, University of WaterlooKühn, StefanStefanKühn0000-0001-7693-350XDeutsches Elektronen-Synchrotron DESYUrbach, CarstenCarstenUrbach0000-0003-1412-7582Helmholtz Institute for Radiation and Nuclear Physics (HISKP) and Bethe Center for Theoretical Physics (bctp), Rheinische Friedrich-Wilhelms-Universität Bonnbonndata2025PhysicsGroß, Christiane FranziskaChristiane FranziskaGroßUniversity of Bonn2025-08-112025-08-202022-01/2025-032503.11480v112306263910text/plainapplication/zip1.0At 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.R, 4.1.2C++, C++17Deutsche ForschungsgemeinschaftCRC 1639 NuMeriQS – project no. 511713970MKW NRWNRW-FAIR, funding code NW21-024-AMinistry of Science, Research and Culture of the State of BrandenburgCenter for Quantum Technology and Applications (CQTA)European Union’s Horizon Europe Framework Programme (HORIZON) under the ERA Chair schemegrant agreement no. 101087126