2007/10/31 by Kenji Harada, Yuto Kuge
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Diffusion #Diffusion Monte Carlo #Dynamic Monte Carlo method #Imaginary time #Line (geometry) #Markov chain Monte Carlo #Mathematics #Monte Carlo method #Monte Carlo molecular modeling #Physics #Quantum #Quantum Monte Carlo #Quantum dynamics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Statistics #The Imaginary #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1143/jpsj.77.013001
published as Journal of the Physical Society of Japan, Vol. 77 No. 1, January, 2008, 013001 (4 pages) · 4 pages, 2 figures, update a reference
openalex publication_date 2008/01/10 · arxiv created 2008/01/11 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The dynamics of samples in the continuous-imaginary-time quantum world-line Monte Carlo simulations with extended ensembles are investigated. In the case of a conventional flat ensemble on the one-dimensional quantum S=1 bi-quadratic model, the asymmetric behavior of Monte Carlo samples appears in the diffusion process in the space of the number of vertices. We prove that a local diffusivity is asymptotically proportional to the number of vertices, and we demonstrate the asymmetric behavior in the flat ensemble case. On the basis of the asymptotic form, we propose the weight of an optimal ensemble as 1/√(n), where n denotes the number of vertices in a sample. It is shown that the asymmetric behavior completely vanishes in the case of the proposed ensemble on the one-dimensional quantum S=1 bi-quadratic model.