Abstract
We use the self consistent harmonic approximation together with the Linear Response Theory to study the effect of nonmagnetic disorder on spin transport in the quantum diluted two-dimensional anisotropic Heisenberg model with spin S=1 in a square lattice. The model has a BKT transition at zero dilution. We calculate the regular part of the spin conductivity σreg(ω) and the Drude weight DS(T) as a function of the non-magnetic concentration, x. Our calculations show that the spin conductivity drops abruptly to zero at xcSCHA≈0.5 indicating that the system changes from an ideal spin conductor state to an insulator. This value is far above the site percolation threshold xcsite≈0.41. Although the SCHA fails in determining precisely the percolation threshold, both the spin conductivity and the Drude weight show a quite regular behavior inside 0≤x≤xcSCHA indicating that the transition stays in the same universality class all along the interval.
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