Effect of the site dilution on spin transport in the two-dimensional biquadratic Heisenberg model

•We have analysed the influence of site dilution in the critical properties.•The site dilution generates a decreases in the inclination of the gap Δ in function of −β.•The Gap extinguishes in the concentration x of non-magnetic impurities x=0.5.•We have verified the influence of the site dilution in the spin transport properties.

We use the SU(3) Schwinger's boson theory to study the spin transport in the biquadratic Heisenberg chains in a square lattice with a distribution of non-magnetic impurities on the lattice. We verify the influence of the site dilution in the Ac and Dc spin conductivities of this model in the Bose–Einstein condensation regime in which the bosons t are condensed. Our results show that the decreasing of the gap Δ with −β suffers a change for different concentrations x of non-magnetic impurities, however the point (in the −β axis) where the gap cancels does not change with x. Therefore, the size of the region ω, where the spin conductivity goes to zero decreases with the increase of x until the point where x=0.5, where the size of this region tends to zero.