Quantum renormalization of the XY model

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Abstract
The statistical mechanics of the two‐dimensional ferromagnetic model with easy‐plane anisotropy is approached by the pure‐quantum self‐consistent harmonic approximation (PQSCHA), that reduces the calculation of thermodynamic averages to effective classical expressions. In the PQSCHA, the quantum corrections to the classical thermodynamics are reduced to suitable (temperature‐dependent) renormalizations of the interaction parameters, so that the full role of the nonlinear excitations is preserved. A particular case is the XX0 model (also known as the quantum XY model), which undergoes a Kosterlitz–Thouless phase transition at some finite temperature Tc. Since it is possible to calculate how much the effective exchange interaction is weakened by quantum fluctuations, we can predict, for instance, the corresponding amount of reduction of Tc for any value of the spin. Even in the extreme quantum case of the spin‐1/2 model, our result is compatible with the estimates of Tc obtained by other authors.