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Improved honeycomb and hyperhoneycomb lattice Hamiltonians for quantum simulations of non-Abelian gauge theories

Marc Illa*, Martin J. Savage†,‡, and Xiaojun Yao§

  • InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, Washington 98195, USA

  • *Contact author: marcilla@uw.edu
  • †Contact author: mjs5@uw.edu
  • ‡On leave from the Institute for Nuclear Theory.
  • §Contact author: xjyao@uw.edu
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Phys. Rev. D 111, 114520 – Published 26 June, 2025

DOI: https://doi.org/10.1103/3rwf-f844

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 O(b2)-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 (nonchiral) hyperhoneycomb as a candidate spatial tessellation for 3+1D quantum simulations of gauge theories, and determined the associated O(b)-improved Hamiltonian.

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Phys. Rev. D 111, 114520– Published 26 June, 2025
  • Received 31 March 2025
  • Accepted 27 May 2025
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