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A spin version of dynamical mean-field theory is extended for magneticallyordered states in the Heisenberg model. The self-consistency equations aresolved with high numerical accuracy by means of the continuous-time quantumMonte Carlo with bosonic baths coupled to the spin. The resultant solution iscritically tested by known physical properties. In contrast with the mean-fieldtheory, soft paramagnons appear near the transition temperature. Moreover, theNambu-Goldstone mode (magnon) in the ferromagnetic phase is reproducedreasonably well. However, antiferromagnetic magnons have an energy gap incontradiction to the Nambu-Goldstone theorem. The origin of this failure isdiscussed in connection with an artificial first-order nature of thetransition.

Dynamical mean-field theory for quantum spin systems: Test of solutions for magnetically ordered states