Real-space renormalization group for two-dimensional quantum spin systems

A. Drzewiński, J. Szṅajd

涼二 宮崎, Ryoji Miyazaki

Fernando Dantas Nobre

Gene F. Mazenko, Enis Oḡuz

C. Y. Pan, H. Q. Lin

By applying a unified real space renormalization group (URG) mapping method, we study the one-dimensional spin-1/2 Ising model with a transverse field (ITF). Unlike the other real space renormalization group methods, the URG method describes the properties of the model at both zero and finite temperatures in a unified way. The results obtained are in good agreement with that obtained by other methods. Application of the URG method to other quantum spin systems is discussed.

Attilio L. Stella, Flavio Toigo

A new formulation of the renormalization-group in real space, suitable for quantum spin systems is proposed. The method is applied to the two-dimensional spin-$\frac{1}{2}$ $X\ensuremath{-}Y$ model on a triangular lattice, the renormalization-group transformation being evaluated up to second order in an appropriate cumulant expansion. To first order an unstable fixed point of the transformation is found, corresponding to a critical temperature and critical indices in satisfactory qualitative agreement with present high-temperature series expansion estimates. In the second-order calculation, however, this fixed point disappears, thus throwing some doubt on the conventional picture of criticality as furnished by high-temperature series. The free energy of the model is also computed. For relatively small values of the nearest-neighbor coupling it is in good agreement with that found by high-temperature series analysis.