Coarse-grained loop algorithms for Monte Carlo simulation of quantum spin systems

Recently, Syljuåsen and Sandvik [Phys. Rev. E. (to be published)] proposed a new framework for constructing algorithms of quantum Monte Carlo simulation. While it includes new classes of powerful algorithms, it is not straightforward to find an efficient algorithm for a given model. Based on their framework, we propose an algorithm that is a natural extension of the conventional loop algorithm with the split-spin representation. A complete table of the vertex density and the worm-scattering probability is presented for the general $\mathrm{XXZ}$ model of an arbitrary S with a uniform magnetic field.