Using generalized Parisi's replica symmetry breaking scheme, the quantum spin glass theory proposed by our previous work is extended to the first-step replica symmetry breaking. A set of new self-consistent equations of spin self-interact ions and spin glass order parameters are obtained. The corresponding local susceptibility is reduced. It is found that the replica symmetry solution for vector spin glass model at low temperature must be broken through calculating the free-energy of the replica symmetry breaking.
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