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

TL;DR

This paper investigates the properties of Majorana edge states in Z2 topological models, revealing gapless states with nodal points under translational symmetry and gapped states without it.

Contribution

It provides a detailed analysis of symmetry-protected Majorana edge states in Wen-plaquette and toric-code models, including their dispersion characteristics.

Findings

Majorana edge states are gapless with nodal points at k=0 and pi under translational symmetry.

Edge states become gapped when translational symmetry is broken.

The study enhances understanding of topological edge modes in Z2 topological orders.

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.