Testing the $\mathrm{SU}(2)$ lattice Hamiltonian built from $S_3$ partitionings
High Energy Physics - Lattice
2023-11-28 v1 Quantum Physics
Abstract
We test a possible digitization of lattice gauge theories based on partitionings of the sphere . 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.
Keywords
Cite
@article{arxiv.2311.15926,
title = {Testing the $\mathrm{SU}(2)$ lattice Hamiltonian built from $S_3$ partitionings},
author = {Marco Garofalo and Tobias Hartung and Timo Jakobs and Karl Jansen and Johann Ostmeyer and Dominik Rolfes and Simone Romiti and Carsten Urbach},
journal= {arXiv preprint arXiv:2311.15926},
year = {2023}
}