Preprint

PUBDB-2023-07713

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Testing the $\mathrm{SU}(2)$ lattice Hamiltonian built from $S_3$ partitionings

Garofalo, M. (Corresponding author) ; Hartung, T. ; Jakobs, T. ; Jansen, K.DESY* ; Ostmeyer, J. ; Rolfes, D. ; Romiti, S. (Corresponding author)Extern* ; Urbach, C.

2023

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Please use a persistent id in citations: doi:10.3204/PUBDB-2023-07713

Report No.: arXiv:2311.15926

Abstract: We test a possible digitization of $\mathrm{SU}(2)$ lattice gauge theories based on partitionings of the sphere $S_3$. In our construction the link operators are unitary and diagonal, with eigenvalues determined by the vertices of the partitioning. The canonical momenta are finite difference operators approximating the Lie derivatives on the manifold. In this formalism we implement the standard Wilson Hamiltonian. We show results for a 2-site Schwinger-type model in 1D and a single-plaquette system in 2D. Our calculations are performed on a classical computer, though in principle they can be implemented also on a quantum device.

Keyword(s): derivative, Lie ; Hamiltonian ; quantum device ; unitarity ; site ; sphere ; lattice field theory ; computer ; lattice

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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)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2023

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