Simple Hamiltonian for Quantum Simulation of Strongly Coupled 2+1D SU(2) Lattice Gauge Theory on a Honeycomb Lattice

Abstract: We find a simple spin Hamiltonian to describe physical states of $2+1$ dimensional SU(2) lattice gauge theory on a honeycomb lattice with a truncation of the electric field representation at $j_{\rm max}=\frac{1}{2}$. The simple spin Hamiltonian only contains local products of Pauli matrices, even though Gauss's law has been completely integrated out.