SciPost Phys. 14, 087 (2023) ·
published 1 May 2023
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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 ν species of Majorana fermions coupled to a static Z2 gauge field. Here each species of Majorana fermions gives rise to an energy band that carries a Chern number C=1, yielding a total Chern number C=ν. It has been shown that the ground states are three (four)-fold topologically degenerate on a torus, when ν is an odd (even) number. These exactly solvable models can be achieved by quantum simulations.
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