Preprint

PUBDB-2025-01008

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Matching Lagrangian and Hamiltonian Simulations in (2+1)-dimensional U(1) Gauge Theory

Gross, C. (Corresponding author)Extern* ; Romiti, S. ; Funcke, L. ; Jansen, K.DESY* ; Kan, A. ; Kuehn, S. (Corresponding author)DESY* ; Urbach, C.

2025

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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-01008

Report No.: arXiv:2503.11480

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.

Note: 11 figures, 9 tables

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Contributing Institute(s):

1. Centre f. Quantum Techno. a. Application (CQTA)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. DFG project G:(GEPRIS)511713970 - SFB 1639: NuMeriQS: Numerische Methoden zur Untersuchung von Dynamik und Strukturbildung in Quantensystemen (511713970) (511713970)
3. QUEST - QUantum computing for Excellence in Science and Technology (101087126) (101087126)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2025

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Database coverage:
; ; Published

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article Groß, C. F. (Corresponding author) ; Romiti, S. ; Funcke, L. ; Jansen, K.DESY* ; Kan, A. ; Kühn, S.DESY* ; Urbach, C.
Matching Lagrangian and Hamiltonian simulations in (2+1)-dimensional U(1) gauge theory
The European physical journal / C 85(11), 1253 (2025) [10.1140/epjc/s10052-025-14923-2]2025     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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