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arXiv · 2209.14333

Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry

Dmitry Green·Claudio Chamon
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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.

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Dmitry Green, Claudio Chamon. 2022-09-28. Constructing Non-Abelian Quantum Spin Liquids Using Combinatorial Gauge Symmetry. https://doi.org/10.21468/scipostphys.15.2.067

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