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

Abstract

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 an artificial first-order nature of the transition.

8 pages, 5 figures

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• Quantum phase transitions in the Bose-Fermi Kondo model
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• Thermodynamic consistency of the charge response in dynamical mean-field based approaches
• Interacting topological Dirac magnons
• Non-linear bond-operator theory and 1/d expansion for coupled-dimer magnets II: Antiferromagnetic phase and quantum phase transition
• Quantum Monte Carlo simulation of spin-boson models using wormhole updates
• Dynamic mean-field theory for dense spin systems at infinite temperature
• Magnon-Magnon Interactions in O(3) Ferromagnets and Equations of Motion for Spin Operators
• Dipolar ordering transitions in many-body quantum optics: Analytical diagrammatic approach to equilibrium quantum spins
• Quantum mean-field approximation for lattice quantum models: truncating quantum correlations, and retaining classical ones