Cluster Monte Carlo algorithm for the quantum rotor model

We propose a highly efficient “worm”-like cluster Monte Carlo algorithm for the quantum rotor model in the link-current representation. We explicitly prove detailed balance for the algorithm even in the presence of disorder. For the pure quantum rotor model with $\mu =0,$ the algorithm yields high- precision estimates for the critical point $K_c=0.333\mathrm{}05\left(5\right)\mathrm{}$ and the correlation length exponent $\nu =0.670\mathrm{}\left(3\right).$ For the disordered case, $\mu =\frac{1}{2}\pm \frac{1}{2},$ we find $\nu =1.15\mathrm{}\left(10\right).$