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Leonardo dos Santos Lima has completed his PhD at the age of 31 years from Universidade Federal de Minas Gerais - Brazil and postdoctoral studies from Tecnische Universität Kaiserslautern, Germany. He is professor of physics of Departamento de Física e Matemática Centro Federal de Educação Tecnológica de Minas Gerais. He has published more than 40 papers in international journals .
We use the Self Consistent Harmonic Approximation together with the Kubo formalism of the linear response theory to study the spin transport in the two-dimensional frustrated Heisenberg anti-ferromagnet in a square lattice with easy-plane ion single anisotropy. The regular part of the spin conductivity ?reg???? is determined for several values of the critical ion single parameter Dc, which separates the low D region from the large D quantum paramagnetic phase. We have obtained an abrupt change in the spin conductivity in the discontinuity points of the graphic Dc vs. ?, where the system presents a quantum phase transition.