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The dynamics of samples in the continuous-imaginary-time quantum world-lineMonte Carlo simulations with extended ensembles are investigated. In the caseof a conventional flat ensemble on the one-dimensional quantum S=1 bi-quadraticmodel, the asymmetric behavior of Monte Carlo samples appears in the diffusionprocess in the space of the number of vertices. We prove that a localdiffusivity is asymptotically proportional to the number of vertices, and wedemonstrate the asymmetric behavior in the flat ensemble case. On the basis ofthe asymptotic form, we propose the weight of an optimal ensemble as$1/\sqrt{n}$, where $n$ denotes the number of vertices in a sample. It is shownthat the asymmetric behavior completely vanishes in the case of the proposedensemble on the one-dimensional quantum S=1 bi-quadratic model.

Diffusion in the Continuous-Imaginary-Time Quantum World-Line Monte Carlo Simulations with Extended Ensembles