2015/01/29 by Mohammad Hossein Zarei · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.91.022319
published as Phys. Rev. A. 91, 022319 (2015) · 15 pages, 12 figures, 1 table, Accepted for publication in Physical Review A
arxiv created 2015/01/29 · arxiv updated 2015/06/23
We study the phase transition from two different topological phases to the ferromagnetic phase by focusing on points of the phase transition. To this end, we present a detailed mapping from such models to the Ising model in a transverse field. Such a mapping is derived by re-writing the initial Hamiltonian in a new basis so that the final model in such a basis has a well-known approximated phase transition point. Specifically, we consider the toric codes and the color codes on some various lattices with Ising perturbation. Our results provide a useful table to compare the robustness of the topological codes and to explicitly show that the robustness of the topological codes depends on triangulation of their underlying lattices.