Abstract
We have propose the Meissner mechanism for the spin supercurrent in quantum spin systems. Besides, we study the behavior of the AC spin conductivity in neighborhood of quantum phase transition in a frustrated spin model such as the antiferromagnet in the union jack lattice with single ion anisotropy at T=0. We investigate the spin conductivity for this model that presents exchange interactions J1 and J2. Our results show a single peak for the conductivity with the height varying with the behavior of critical anisotropy Dc with J2. We obtain the conductivity tending to zero in the limit ω→0.
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