Topological aspects of an exactly solvable spin chain

Abstract

We analyse a spin-1/2 chain with two-spin interactions which shown to exactly solvable by Lieb, Schultz and Mattis. We show that the model can be viewed as a generalised Kitaev model that is analytically solvable for all defect sectors. We present an alternate proof that the defect free sector is the ground state, which is valid for a larger parameter range. We show that the defect sectors have degenerate ground states corresponding to unpaired Majorana fermion modes and that the degeneracy is topologically protected against disorder in the spin-spin couplings. The unpaired Majorana fermions can be manipulated by tuning the model parameters and can hence be used for topological quantum computation.

References in corpus (2)

• Non-Abelian Anyons and Topological Quantum Computation
• An exact chiral spin liquid with non-Abelian anyons

Cited by in corpus (5)

• Topologically protected localised states in spin chains
• Robust Quantum Entanglement Generation and Generation-plus-Storage Protocols with Spin Chains
• Energy dynamics in the Heisenberg-Kitaev chain
• Topological transitions in a model with Particle-Hole symmetry, Pancharatnam-Berry Curvature and Dirac Points
• Slave fermion formalism for the tetrahedral spin chain