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

• URL: http://arxiv.org/abs/2503.09688v1
• Date: Wed, 12 Mar 2025 18:00:01 GMT
• Title: Improved Honeycomb and Hyper-Honeycomb Lattice Hamiltonians for Quantum Simulations of Non-Abelian Gauge Theories
• Authors: Marc Illa, Martin J. Savage, Xiaojun Yao,
• Abstract summary: Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed.<n>For the honeycomb lattice, we derive a classically $cal O(b2)$-improved Hamiltonian, with $b$ being the lattice spacing.<n>We have identified the (non-chiral) hyper-honeycomb 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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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed for honeycomb (2+1D) and hyper-honeycomb (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) hyper-honeycomb 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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