Influence of quantum phase transition on spin transport in the quantum antiferromagnet in the honeycomb lattice

We use the SU(3) Schwinger boson theory to study the spin transport properties of the two-dimensional anisotropic frustrated Heisenberg model in a honeycomb lattice at T=0 with single ion anisotropy and third neighbor interactions. We have investigated the behavior of the spin conductivity for this model that presents exchange interactions J1, J2 and J3. We study the spin transport in the Bose-Einstein condensation regime where the bosons tz are condensed. Our results show an influence of the quantum phase transition point on the spin conductivity behavior. We also have made a diagrammatic expansion for the Green-function and did not obtain any significant change of the results.