New generation of Diagrammatic Monte Carlo methods

EPSRC：康纳勒尼汉：EP/R513064/1该项目的目标是将各自的优势结合联合收割机来解决量子多体问题，该问题的名称是指由于涉及大量粒子（如材料）而无法通过常规方法解决的量子力学方程问题。为了解决这个问题，一个抽象的数学形式主义被开发出来，这需要先进的数值算法，实现和计算机上的大规模计算。我们将试图把两个最有前途的算法，建立良好的Diagrammatic Monte Carlo方法，和最近发现的Matsubara积分（AMI）的关键优势。产生的新技术将使物理学家能够可靠地描述和控制最具挑战性和最重要的强电子相关现象，这些现象以前是任何最先进的方法都无法解决的问题。

EPSRC : Connor Lenihan : EP/R513064/1The goal of this project is to combine the respective strengths two novel, complementary approaches to solving the Quantum Many Body Problem, the name given to the problem of the equations of quantum mechanics becoming impossible to solve by conventional methods due to very large numbers of particles being involved, such as in materials. To deal with this, an abstract mathematical formalism was developed, which requires advanced numerical algorithms, implementation and large-scale calculations on a computer. We will attempt to bring together the key advantages of two pf the most promising algorithms, the well- established Diagrammatic Monte Carlo method, and the more recently discovered Algorithmic Matsubara Integration (AMI). The new technique produced will allow physicists to reliably describe and control the most challenging, and most important, phenomena of strong electron correlations in a class of problems previously out of reach for any state of the art method.