Citation: Chulliparambil, Sreejith, et al. "Microscopic models for Kitaev's sixteenfold way of anyon theories." Physical Review B 102.20 (2020): 201111.
Web: https://arxiv.org/abs/2005.13683
Tags: Invertible-phases, Majorana-fermions, Toric-code
This paper is the culmination of a lot of work. Two dimensional topological insulators are classified by their Chern number, which is some integer "nu". In his seminar 2006 paper, Kitaev shows that when a 2D topological insulator is coupled to a Z2 gauge field it can generate genuine topological order (not fermionic or symmetry protected). Moreover, he observed that the bulk anyons should only depend on nu modulo 16. However, he only constructed models for nu=0 and nu=+-1. It has been an outstanding challenge to construct exactly soluble models for other values of nu, and confirm that they have the expected anyon content. Incremental progress has been made over the last decade or so, notably in this paper:
> Zhang, Shang-Shun, Cristian D. Batista, and Gábor B. Halász. "Toward Kitaev's sixteenfold way in a honeycomb lattice model." Physical Review Research 2.2 (2020): 023334.
The present paper claims that they have a general construction for all values of nu. One of the hey technical insights underlying this paper is the earlier work of Nielsen, Cirac, and Sierra:
> Nielsen, Anne EB, J. Ignacio Cirac, and Germán Sierra. "Laughlin spin-liquid states on lattices obtained from conformal field theory." Physical review letters 108.25 (2012): 257206.
In this paper it is (implicitly) conjectured that the bulk of the nu-Kitaev spin liquid has boundary CFT the SO(16)_1 Wess-Zumino-Witten model. From then, using standard bulk-edge correspondence to construct bulk wavefunctions. In the present paper, they push these ideas further by making exactly solvable local Hamiltonains. These Hamiltonians have a global SO(nu) symmetry. They are put on the square lattice for even nu, and on the hexagonal lattice for odd nu. Note that the onsite Hilbert space dimensions grow exponentially, so for nu=16 you need 512 dimensional on-site Hilbert spaces.
One reason to find these models interesting is that by gauging away the anyons in the nu=16 state you get a version of the E8 state, which is an important and intriguing state.