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The SU(2) slave boson formulation of the bond-type spin quadratic orders is developed, where the bond-type nematic states are described as the RVB state of spin-triplet valence bond. The d-vector of the spin-triplet pairing plays role of the director vector of the spin nematic state. The low energy excitation around such an ansatz generally comprises the (potentially massless) gauge boson, massless goldstone boson and spinon indivisual excitations. Extending the Wen's (non-)collinearity arguments of the SU(2) gauge flux to the spin-triplet ansatz, one can readily idenitify the number of massless gauge modes out of the ivariant gauge group (IGG). Armed with these knowledge, we (i) enumerate possible mean field ansatz for the J_1-J_2 ferromagnetic frustrated Heisenberg model (ferromagnetic J_1 and antiferromagnetic J_2) and (ii) argue their stabilities against the confinement effect. Thereby, we found that the spinon analogue of the Balian-Werthamer state becomes its stable Z_2 state, which precisely corresponds to the bond-type spin-nematic ordered state found by the previous ED studies [Phys. Rev. Lett. {\bf 96}, 027213 (2006)]. |
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