Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Abstract

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.

arXiv comment9 pages, 4 figures. Minor edits to make exposition clearer in some places

References in corpus (9)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry
• Non-perturbative gadget for topological quantum codes
• Topological Quantum Liquids with Quaternion Non-Abelian Statistics
• A superconducting circuit realization of combinatorial gauge symmetry
• Abelian combinatorial gauge symmetry

Cited by in corpus (1)

• $U(1)$ symmetry-enriched toric code