SciPost logo

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

Jin-Tao Jin, Jian-Jian Miao, Yi Zhou

SciPost Phys. 14, 087 (2023) · published 1 May 2023


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 species 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.

Cited by 1

Crossref Cited-by

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.
Funders for the research work leading to this publication