A quantum Monte Carlo algorithm realizing an intrinsic relaxation

We propose a new quantum Monte Carlo algorithm that realizes a relaxation intrinsic to an original quantum system. The Monte Carlo dynamics satisfies the dynamic scaling relation τ ∼ ξ^z and is independent of the Trotter number. The finiteness of the Trotter number appears as the finite-size effect. An infinite Trotter number version of the algorithm, which enables us to observe a true relaxation of the original system, is also formulated. The strategy of the algorithm is a compromise between a conventional worldline local flip and a modern cluster loop flip. It is a local flip in the real-space direction and is a cluster flip in the Trotter direction. The new algorithm is tested using the transverse-field Ising model in two dimensions. An accurate phase diagram is obtained.