Spin transport in the two-dimensional quantum disordered anisotropic Heisenberg model

•The site dilution generates a large influence on regular part of the spin conductivity, σreg(ω)σreg(ω), and in the Drude weight, D(T).•In a concentration of impurities about x≈0.5x≈0.5, the regular part of the spin conductivity and the Drude weight fall to zero.•In this point we have a change in the state of the system from an ideal spin conductor to a spin insulator.

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)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.