Abstract
We study an exactly solvable toric code type of Hamiltonian in three dimensions, defined on the diamond lattice with spin- degrees of freedom at each site. The Hamiltonian is a sum of mutually commuting plaquette operators , all of which have eigenvalue +1 in the ground state. The excitations are “fluxes,” which are plaquettes with . Due to certain local kinematic constraints, fluxes form loops. The elementary flux-loop excitations are fermions, in contrast to other solvable spin- models in three dimensions, where the excitations are bosons. Furthermore, the flux loops braid nontrivially, giving rise to Abelian anyonlike statistics.
- Received 15 May 2014
- Revised 21 July 2014
DOI:https://doi.org/10.1103/PhysRevB.90.104424
©2014 American Physical Society