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@ARTICLE{Gross:625035,
      author       = {Gross, Christoph and Romiti, S. and Funcke, L. and Jansen,
                      Karl and Kan, A. and Kuehn, Stefan and Urbach, C.},
      title        = {{M}atching {L}agrangian and {H}amiltonian {S}imulations in
                      (2+1)-dimensional {U}(1) {G}auge {T}heory},
      reportid     = {PUBDB-2025-01008, arXiv:2503.11480},
      year         = {2025},
      note         = {11 figures, 9 tables},
      abstract     = {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.},
      cin          = {CQTA},
      cid          = {I:(DE-H253)CQTA-20221102},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)511713970 - SFB 1639: NuMeriQS: Numerische
                      Methoden zur Untersuchung von Dynamik und Strukturbildung in
                      Quantensystemen (511713970) / QUEST - QUantum computing for
                      Excellence in Science and Technology (101087126)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)511713970 /
                      G:(EU-Grant)101087126},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2503.11480},
      howpublished = {arXiv:2503.11480},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2503.11480;\%\%$},
      doi          = {10.3204/PUBDB-2025-01008},
      url          = {https://bib-pubdb1.desy.de/record/625035},
}