On the real-space renormalization-group study of some 2D quantum spin systems

Abstract

Abstract Within a real-space renormalization-group framework, the critical behaviour of the spin- 1 2 anisotropic quantum Heisenberg model on the three planar lattices has been studied. To examine the stability of the results with respect to changes in the approximation scheme, various divisions of the lattices and various truncation procedures have been used. It has been shown that there is a non-trivial fixed point and corresponding critical temperature for the nearest-neighbour XY model for each two-dimensional lattice irrespective of the approximation used. Concerning the Heisenberg model, to first order in the cumulant expansion there is no non-trivial fixed point, however, it appears in the second- and third-order calculations. This suggests that the two-dimensional Heisenberg model also exhibits some kind of a critical behaviour. In addition, the phase transitions to the many-sublattice structure have been discussed.