Study of Quantum Spin Systems using Real Space Renormalization Transformations

Abstract

The spin 1/2 anisotropic Heisenberg model is studied by means of the real space renormalization transformations. Thermodynamic properties of one-dimensional systems are calculated by using an approximate decimation method. These results agree well with those obtained by Bonner and Fisher and by Katsura. Two- and three-dimensional systems are studied by generalizing the Migdal-Kadanoff renormalization transformations to quantum spin systems. For the Ising and Heisenberg models in two and three dimensions and for the X-Y model in three dimensions, the critical properties thus obtained are in qualitative agreement with those obtained from high temperature series expansions. For the two-dimensional X-Y model, our results suggest that this model undergoes some kind of phase transition and that the critical behaviour of this model is similar to that expected for the classical X-Y and planar models.