Majorana Edge States for Z2 Topological Orders of the Wen-plaquette Model and the Toric-code Model

Abstract

In this paper we study the symmetry protected Majorana edge states for the Z2 topological order of the Wen-plaquette model and the toric-code model and calculate the dispersion of the Majorana edge states. For the system with translational symmetry, the Majorana edge states are gapless and have the nodal points at k=0 and k=pi. For the edge states of the toric-code model without translational symmetry, the edge modes become gapped.

9 pages, 12 figures

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• Exact description of the boundary theory of the Kitaev Toric Code with open boundary conditions
• Geometric and computational aspects of chiral topological quantum matter
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• Spin chains, defects, and quantum wires for the quantum-double edge