Constructing non-Abelian quantum spin liquids using combinatorial gauge symmetry

We construct Hamiltonians with only 1-and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic ZZ interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry.

Automated summary

We have constructed Hamiltonians that show an exact non-Abelian gauge symmetry with only 1-and 2-body interactions. Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It is an explicit example of a spin Hamiltonian that has no sign problem and achieves a non-Abelian topological phase. Additionally, we propose a superconducting quantum circuit version with the same symmetry.