Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Understand

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.