Geometric Approach to Markov Chain Monte Carlo

将填埋法等几何方法应用于强相关多体系统中最有效的马尔可夫链蒙特卡罗方法，发现了一种能显著加速马尔可夫链收敛的通用方法。我们还开发了一种精确的能隙估计方法，量子蒙特卡罗能级光谱，计算局部Z_N Berry相位的方法，以及具有强空间各向异性的系统的新的有限尺寸标度方法。此外，我们还开发并公开了垃圾填埋方法的通用库BCL库和基于BCL库的量子蒙特卡罗应用程序Worms包。

We have applied geometric approaches, such as the landfilling method, to the Markov chain Monte Carlo method, which is one of the most powerful method to strongly correlated many-body systems, and found a generic method that drastically accelerates the convergence of Markov chain. We have also developed a precise estimator of energy gap, quantum Monte Carlo level spectroscopy, method for calculating the local Z_N Berry phase, new finite size scaling method for systems with strong spatial anisotropy. In addition, we have developed and made public the BCL library - the generic library for the landfilling method, and the Worms Package - the quantum Monte Carlo application based on the BCL library.