Effect of quantum phase transition on spin transport in the spatially frustrated Heisenberg model

We have used the Schwinger's boson theory to study the spin transport in the anisotropic two-dimensional spatially frustrated Heisenberg antiferromagnetic model in the square lattice. Our results show a sudden change in the AC spin conductivity σreg(ω) in the quantum phase transition point, where we have the gap of the system going to zero at critical point Dc=0. We have found a sudden change for a superconductor state in the DC limit ω→0 independent of the value of the Drude's weight found in the quantum phase transition point. Away from it, we have obtained that the behavior of the spin conductivity changes for single peak at ω=ωp and in this case, σreg(ω) goes to zero in small ω and large ω limits.