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

TL;DR

This paper extends dynamical mean-field theory to magnetically ordered quantum spin systems, solving self-consistency equations with quantum Monte Carlo and testing physical properties, revealing both successes and limitations of the approach.

Contribution

It introduces a spin version of dynamical mean-field theory for ordered states and demonstrates its application using quantum Monte Carlo methods.

Findings

Soft paramagnons appear near the transition temperature.

The magnon mode in ferromagnetic phase is well reproduced.

Antiferromagnetic magnons show an energy gap, contradicting the Nambu-Goldstone theorem.

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.