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

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 $\mathcal{O}(b^2)$-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 $\mathcal{O}(b)$-improved Hamiltonian.

12 pages, 8 figures, 3 tables, and a Mathematica Notebook as Supplemental Material; published version