Spin conductivity of the two-dimensional anisotropic frustrated Heisenberg model in the honeycomb lattice

•We have analyzed the honeycomb model.•We use the Kubo formalism to calculate the spin conductivity using SU3 Schwinger boson.•We have analyzed the spin transport properties of the model.

We use the SU(3) Schwinger׳s boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0. We have investigated the behavior of the spin conductivity for this model which presents a single-ion anisotropy and J1 and J2 exchange interactions. We study the spin transport in the Bose–Einstein condensation regime where we have that the tz bosons are condensed and the following condition is valid: 〈tz〉=〈tz†〉=t. Our results show a metallic spin transport for ω>0ω>0 and a superconductor spin transport in the limit of DC   conductivity, ω→0ω→0, where σ(ω)σ(ω) tends to infinity in this limit of ω.