Quantum effects on the Berezinskii-Kosterlitz-Thouless transition in the ferromagnetic XXZ model

The quantum easy-plane ferromagnetic 2D XXZ model is approached by the pure-quantum self-consistent harmonic approximation, that reduces it to an effective classical model. Quantum fluctuations weaken both the effective exchange, leading to a reduced Berezinskii-Kosterlitz-Thouless transition temperature with respect to the classical model, and the effective easy-plane anisotropy. The latter vanishes when the anisotropy is smaller than a cut-off value, leading to an instability that could be interpreted as a crossover to a strongly quantum regime where a picture of classical-like renormalized vortices is inadequate.