Migdal-Kadanoff renormalization group approach to the spin-1/2 anisotropic Heisenberg model

The spin-1/2 anisotropic Heisenberg model is studied by generalizing the Migdal-Kadanoff renormalization transformations to quantum spin systems. An approximate one-dimensional decimation is employed besides the potential-moving approximation in this generalization. It is shown that these approximations are valid at high temperatures. The results obtained from these approximations suggest that the two-dimensional spin-1/2 X-Y model shows the critical behavior similar to that expected for the classical X-Y and planar models.