Topological aspects of an exactly solvable spin chain

TL;DR

This paper explores a solvable spin-1/2 chain model, revealing topologically protected Majorana modes that can be manipulated for quantum computing, extending understanding of topological phases in spin systems.

Contribution

It demonstrates that a generalized Kitaev model with spin interactions is exactly solvable across all defect sectors and shows topological protection of Majorana modes.

Findings

Ground state degeneracy is topologically protected.

Majorana modes can be manipulated via model parameters.

Model extends solvability to all defect sectors.

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.