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

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 σ^reg(ω) and the Drude weight D_S(T) as a function of the non-magnetic concentration, x. Our calculations show that the spin conductivity drops abruptly to zero at x_c^SCHA≈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 x_c^site≈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≤x_c^SCHA indicating that the transition stays in the same universality class all along the interval. - Highlights: • The site dilution generates a large influence on regular part of the spin conductivity, σ^reg(ω), and in the Drude weight, D(T). • In a concentration of impurities about x≈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