Transport and spin Hall conductivity in two-dimensional XY model on lattice

Spin transport is studied in the frustrated two-dimensional XY model on honeycomb lattice. The calculations are performed taking into account next-nearest neighboring interactions J(2) and single-ion anisotropy, using the SU(N) Schwinger boson approach. We consider the effect of next-nearest neighboring exchange interactions J(2J) and interlayer coupling J(?) on continuum conductivity, where at critical line in the phase diagram, the system suffers a quantum phase transition between the Neel phase to paramagnetic phase. The spin Hall conductivity as a function of temperature, in the model with Dzyaloshinskii-Moriya interaction (DMI) is also analyzed.