Constructing non-abelian quantum spin liquids using combinatorial gauge symmetry. (English) Zbl 07905002
Summary: 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.
MSC:
| 81Pxx | Foundations, quantum information and its processing, quantum axioms, and philosophy |
| 82Bxx | Equilibrium statistical mechanics |
| 81Sxx | General quantum mechanics and problems of quantization |
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