Generalized Kitaev spin liquid model and emergent twist defect

Bowen Yan, Penghua Chen, Shawn Xingshan Cui

Ciarán Hickey

H. Takagi, T. Takayama, George Jackeli +2 more

Yan, Bowen, Chen, Penghua, Shawn Xingshan Cui

The Kitaev spin liquid model on honeycomb lattice offers an intriguing feature that encapsulates both Abelian and non-Abelian anyons. Recent studies suggest that the comprehensive phase diagram of possible generalized Kitaev model largely depends on the specific details of the discrete lattice, which somewhat deviates from the traditional understanding of "topological" phases. In this paper, we propose an adapted version of the Kitaev spin liquid model on arbitrary planar lattices. Our revised model recovers the toric code model under certain parameter selections within the Hamiltonian terms. Our research indicates that changes in parameters can initiate the emergence of holes, domain walls, or twist defects. Notably, the twist defect, which presents as a lattice dislocation defect, exhibits non-Abelian braiding statistics upon tuning the coefficients of the Hamiltonian on a standard translationally invariant lattice. Additionally, we illustrate that the creation, movement, and fusion of these defects can be accomplished through natural time evolution by linearly interpolating the static Hamiltonian. These defects demonstrate the Ising anyon fusion rule as anticipated. Our findings hint at possible implementation in actual physical materials owing to a more realistically achievable two-body interaction.

Zheng-Chuan Wang

Julian May-Mann, Taylor L. Hughes

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 superlattice 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.