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

TL;DR

This paper investigates the diffusion behavior in continuous-imaginary-time quantum Monte Carlo simulations, revealing asymmetries in flat ensembles and proposing an optimal ensemble weight to eliminate these asymmetries.

Contribution

It introduces an optimal ensemble weight of 1/√n to remove asymmetries in sample diffusion in quantum Monte Carlo simulations.

Findings

Asymmetric diffusion behavior observed in flat ensembles.

Proposed ensemble weight of 1/√n effectively removes asymmetry.

Asymptotic analysis links local diffusivity to the number of vertices.

Abstract

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 $1/\sqrt{n}$, 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.