In this paper, we proposed a blockspin scheme and developed the usual cluster-updating algorithms for the one-and two-dimensional quantum spin systems, saying s=1/2 isotropic Hei-senberg models. The results for he ferro-and antiferro-magnet chains showed that the criti-cal slowing down (CSD) was indeed eliminated, and so it offered a possibility to improve the estimations in the lower-temperature region. We expect that the algorithms could also be ap-plied to the anisotropic or/and the higher-spin cases, as will as some other interesting models, such as eight-vortex lattice model and low-dimensional Fermi-systems.
We introduce a natural way to extend celebrated spin-cluster Monte Carlo algorithms for fast thermal lattice simulations at criticality, such as the Wolff algorithm, to systems in arbitrary fields, be they linear magnetic vector fields or nonlinear anisotropic ones. By generalizing the ``ghost spin'' representation to one with a ``ghost transformation,'' global invariance to spin symmetry transformations is restored at the cost of an extra degree of freedom which lives in the space of symmetry transformations. The ordinary cluster-building process can then be run on the representation. We show that this extension preserves the scaling of accelerated dynamics in the absence of a field for Ising, Potts, and
O(n) models and demonstrate the method's use in modeling the presence of novel nonlinear fields. We also provide a c++ library for the method's convenient implementation for arbitrary models.