Zero energy and chiral edge modes in a p-wave magnetic spin model

Abstract

In this work we discuss the formation of zero energy vortex and chiral edge modes in a fermionic representation of the Kitaev honeycomb model. We introduce the representation and show how the associated Jordan-Wigner procedure naturally defines the so called branch cuts that connect the topological vortex excitations. Using this notion of the branch cuts we show how to, in the non-Abelian phase of the model, describe the Majorana zero mode structure associated with vortex excitations. Furthermore we show how, by intersecting the edges between Abelian and non-Abelian domains, the branch cuts dictate the character of the chiral edge modes. In particular we will see in what situations the exact zero energy Majorana edge modes exist. On a cylinder, and for the particular instances where the Abelian phase of the model is the full vacuum, we have been able to exactly solve for the systems edge energy eigensolutions and derive a recursive formula that exactly describes the edge mode structure. Penetration depth is also calculated and shown to be dependent on the momentum of the edge mode. These solutions also describe the overall character of the fully open non-Abelian domain and are excellent approximations at moderate distances from the corners.

arXiv comment6 pages, 5 figures

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Cited by in corpus (12)

• Dynamics of Fractionalization in Quantum Spin Liquids
• Majorana edge modes in the Kitaev model
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Perturbed vortex lattices and the stability of nucleated topological phases
• Topological Blocking in Quantum Quench Dynamics
• Kaleidoscope of topological phases with multiple Majorana species
• Majorana flat band edge modes of topological gapless phase in 2D Kitaev square lattice
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Rigorous Calculations of Non-Abelian Statistics in the Kitaev Honeycomb Model
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Maximal distant entanglement in Kitaev tube
• The Kitaev honeycomb model on surfaces of genus $g\ge 2$