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arXiv · 2209.09054

Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way

Jin-Tao Jin·Jian-Jian Miao·Yi Zhou
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Abstract

A family of two-dimensional (2D) spin-1/2 models have been constructed to realize Kitaev's sixteen-fold way of anyon theories. Defining a one-dimensional (1D) path through all the lattice sites, and performing the Jordan-Wigner transformation with the help of the 1D path, we find that such a spin-1/2 model is equivalent to a model with $\nu$ species of Majorana fermions coupled to a static $\mathbb{Z}_2$ gauge field. Here each specie of Majorana fermions gives rise to an energy band that carries a Chern number $\mathcal{C}=1$, yielding a total Chern number $\mathcal{C}=\nu$. It has been shown that the ground states are three (four)-fold topologically degenerate on a torus, when $\nu$ is an odd (even) number. These exactly solvable models can be achieved by quantum simulations.

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Jin-Tao Jin, Jian-Jian Miao, Yi Zhou. 2022-09-19. Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way. https://doi.org/10.21468/scipostphys.14.5.087

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