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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 truncationof the electric field representation at $j_{\rm max}=\frac{1}{2}$. The simplespin Hamiltonian only contains local products of Pauli matrices, even thoughGauss's law has been completely integrated out.

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