A spin version of dynamical mean-field theory is extended for magnetically ordered states in the Heisenberg model. The self-consistency equations are solved with high numerical accuracy by means of the continuous-time quantum Monte Carlo with bosonic baths coupled to the spin. The resultant solution is critically tested by known physical properties. In contrast with the mean-field theory, soft paramagnons appear near the transition temperature. Moreover, the Nambu-Goldstone mode (magnon) in the ferromagnetic phase is reproduced reasonably well. However, antiferromagnetic magnons have an energy gap in contradiction to the Nambu-Goldstone theorem. The origin of this failure is discussed in connection with the artificial first-order nature of the transition.

• Received 5 June 2013

DOI:https://doi.org/10.1103/PhysRevB.88.024427