Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions

Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical approaches. Based on the stochastic series expansion method, we develop an efficient and exact quantum Monte Carlo "sweeping cluster" algorithm which automatically satisfies the geometrical restrictions. Here we use the quantum dimer model as a benchmark to demonstrate the effectiveness of this algorithm. Comparing to existing numerical methods, we can obtain higher accuracy results for a wider parameter region and much more substantial system sizes(160$\times$160). In particular, we find that the ground state corresponds to the mixture of the columnar phase and plaquette phase for a vast parameter region.