Slave fermion formalism for the tetrahedral spin chain

TL;DR

This paper applies the SU(2) slave fermion formalism to analyze a one-dimensional tetrahedral spin chain, revealing its phase diagram, spin liquid nature, and topological triviality, aligning with previous exact results.

Contribution

It introduces a slave fermion approach to a tetrahedral spin chain and demonstrates its effectiveness in reproducing known phase diagrams and properties.

Findings

Phase diagram matches exact results

Identifies the spin liquid nature of the gapless phase

Model is topologically trivial with no Majorana edge modes

Abstract

We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.