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arXiv · 2503.09688

Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories

Marc Illa·Martin J. Savage·Xiaojun Yao
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Abstract

Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed for honeycomb (2+1D) and hyperhoneycomb (3+1D) spatial tessellations. This is motivated by the desire to identify lattices for quantum simulations that involve only 3-link vertices among the gauge field group spaces in order to reduce the complexity in applications of the plaquette operator. For the honeycomb lattice, we derive a classically ${\cal O}(b^2)$-improved Hamiltonian, with $b$ being the lattice spacing. Tadpole improvement via the mean-field value of the plaquette operator is used to provide the corresponding quantum improvements. We have identified the (non-chiral) hyperhoneycomb as a candidate spatial tessellation for 3+1D quantum simulations of gauge theories, and determined the associated ${\cal O}(b)$-improved Hamiltonian.

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Marc Illa, Martin J. Savage, Xiaojun Yao. 2025-03-12. Improved Honeycomb and Hyperhoneycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories. https://doi.org/10.1103/3rwf-f844

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