Twisted Kitaev Bilayers and the Moiré Ising Model

Abstract

In recent years, there have been numerous examples of twisted bilayer systems that host remarkable physical properties that are not found in their untwisted counterparts. Motivated by this, we study the properties of twisted bilayers of the Kitaev honeycomb model in the Abelian spin liquid phase. We show that for strong, short-ranged, interlayer interactions, a super-lattice of non-Abelian defects forms in the twisted bilayer system. These non-Abelian defects are wormhole-like genons that allow anyons from one layer to tunnel to the other layer. We find that when a magnetic field is applied to the system, the low energy dynamics of the twisted bilayer system can be mapped onto four quantum Ising models arising from the degrees of freedom localized on the genon defects. At small twist angles, the Ising models are in a trivial paramagnetic phase, and at large twist angles, they are in a ferromagnetic phase.

arXiv comment12 pages (10 figures)

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Cited by in corpus (9)

• Floquet-engineering topological transitions in a twisted transition metal dichalcogenide homobilayer
• Kitaev spin-orbital bilayers and their moiré superlattices
• Magic continuum in twisted bilayer square lattice with staggered flux
• Twisted bilayer U(1) Dirac spin liquids
• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
• Magnon bands in twisted bilayer honeycomb quantum magnets
• Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
• Emergent Hyper-Magic Manifold in Twisted Kitaev Bilayers
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices