Quantum correction to the BKT transition for 2D easy-plane antiferromagnets

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Abstract
We consider the quantum antiferromagnet with easy‐plane exchange anisotropy, namely, the antiferromagnetic XXZ model, on the square lattice. Its classical counterpart, compared to the planar model shows a reduction of the critical temperature TBKT of the Berezinskii–Kosterlitz–Thouless phase transition, that is a consequence of the thermal out‐of‐plane fluctuations. For the quantum system we use the pure‐quantum self‐consistent harmonic approximation to calculate how much the effective exchange interaction is weakened as an effect of the pure‐quantum part of the fluctuations. One can then predict the further reduction of TBKT with respect to the corresponding classical system. The theory works well in a wide range of values of the easy‐plane anisotropy. In the extreme case of the spin‐1/2 model, the result is compatible with the estimate of TBKT obtained by previous quantum Monte Carlo simulations. When the anisotropy is weak the theory leads to an unphysical ‘‘isotropization’’ due to the use of the Villain spin‐boson transformation.