Eur. Phys. J. B (2016) 89: 206
https://doi.org/10.1140/epjb/e2016-70084-8

Regular Article

Slave fermion formalism for the tetrahedral spin chain

Harish-Chandra Research Institute, Chhatnag Road, Jhusi, 211019 Allahabad, India

^a e-mail: sumathi@mri.ernet.in

Received: 5 February 2016
Received in final form: 23 June 2016
Published online: 26 September 2016

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.