Exact solution of theZ2Chern-Simons model on a triangular lattice

B. Douçot, L. B. Ioffe
2005 Physical Review A. Atomic, Molecular, and Optical Physics  
We construct the Hamiltonian description of the Chern-Simons theory with Z_n gauge group on a triangular lattice. We show that the Z_2 model can be mapped onto free Majorana fermions and compute the excitation spectrum. In the bulk the spectrum turns out to be gapless but acquires a gap if a magnetic term is added to the Hamiltonian. On a lattice edge one gets additional non-gauge invariant (matter) gapless degrees of freedom whose number grows linearly with the edge length. Therefore, a small
more » ... ole in the lattice plays the role of a charged particle characterized by a non-trivial projective representation of the gauge group, while a long edge provides a decoherence mechanism for the fluxes. We discuss briefly the implications for the implementations of protected qubits.
doi:10.1103/physreva.72.032303 fatcat:6t6idbc6ffg77fb243lqb3lsta