Generalized Kitaev Spin Liquid model and Emergent Twist Defect

TL;DR

This paper introduces a generalized Kitaev spin liquid model on arbitrary lattices, revealing how tuning parameters can produce non-Abelian twist defects with potential for physical realization and topological quantum computation.

Contribution

It extends the Kitaev model to arbitrary planar lattices, demonstrating the emergence of non-Abelian twist defects and their braiding properties within a more realistic two-body interaction framework.

Findings

Twist defects exhibit non-Abelian braiding statistics.

Defects can be created, moved, and fused via Hamiltonian interpolation.

Model recovers toric code as a special case.

Abstract

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.