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-ferromagneti...
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| Format: | Article |
| Language: | English |
| Published: |
SciPost
2023-08-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.2.067 |
| 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. |
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| ISSN: | 2542-4653 |