New methods in the theory of quantum spin systems

T. Oguchi, Hidetsugu Kitatani

Andrei A. Zvyagin

A. Kitazawa

We consider the Gaussian transition of one-dimensional quantum spin systems. Although the Gaussian transition is the second-order phase transition, the usual finite-size scaling technique does not work well in some cases. Using the conformal field theory, we present a new method which overcomes this difficulty.

Jie Yu Wang, Ralf Meyer

Daisuke Yamamoto

Mean-field approaches provide a qualitative understanding of the behavior of interacting many-body systems. Weiss's molecular-field theory, in particular, has been successfully applied to the studies of various phenomena. However, since local fluctuations from the average are ignored, this simple mean-field theory does not work for systems whose distinctive behavior is caused by fluctuation effects. In the present work, we introduce a new cluster mean-field approach, which we refer to as the correlated cluster mean-field approach, and the applications to classical and quantum spin systems are demonstrated. We divide the lattice sites into clusters consisting of several sites and include the effect of cluster-cluster correlations into the effective fields acting on the spins. In doing so, the effect of spin fluctuations can be taken into account, and our method gives qualitatively and even semiquantitatively correct results for both classical and quantum systems.

Hiroshi Takano

On the basis of the path integral representation of the partition function of a quantum spin system, which is derived by Lieb with use of the Bloch coherent state representation, we propose a new Monte Carlo method for quantum spin systems. In this method, the magnitude S of the spin can be varied freely, because S appears in the path integral only as a parameter. The approximation used in this method can be systematically improved by the 1/n-expansion, where n is the additional dimension in the path integral representation. The formulation and some properties of the method are discussed. Simple examples of the application of the method are also presented.