A quantum Monte Carlo algorithm for the transverse Ising model with arbitrary short- or long-range interactions is presented. The algorithm is based on sampling the diagonal matrix elements of the power-series expansion of the density matrix (stochastic series expansion), and avoids the interaction summations necessary in conventional methods. In the case of long-range interactions, the scaling of the computation time with the system size N is therefore reduced from $N^2$ to $N\ln \mathrm{}\left(N\right).$ The method is tested on a one-dimensional ferromagnet in a transverse field, with interactions decaying as ${1/r}^2.$

• Received 27 March 2003

DOI:https://doi.org/10.1103/PhysRevE.68.056701