Affiliation:
1. Kavli Institute for Theoretical Physics
2. Chinese University of Hong Kong
3. Chinese Academy of Sciences
4. Songshan Lake Materials Laboratory
5. University of Chinese Academy of Sciences
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 \nuν species of Majorana fermions coupled to a static \mathbb{Z}_2ℤ2 gauge field. Here each species of Majorana fermions gives rise to an energy band that carries a Chern number \mathcal{C}=1𝒞=1, yielding a total Chern number \mathcal{C}=\nu𝒞=ν. It has been shown that the ground states are three (four)-fold topologically degenerate on a torus, when \nuν is an odd (even) number. These exactly solvable models can be achieved by quantum simulations.
Funder
Chinese Academy of Sciences
Chinese University of Hong Kong
K. C. Wong Education Foundation
National Key Research and Development Program of China
National Natural Science Foundation of China
Research Grants Council, University Grants Committee
Subject
General Physics and Astronomy