New generation of Diagrammatic Monte Carlo methods

该项目的目标是结合各自的优势，两种新颖的，互补的方法来解决量子多体问题，量子多体问题的名称是量子力学方程的问题，由于涉及到非常大量的粒子，例如在材料中，用传统方法无法解决。为了解决这个问题，一个抽象的数学形式被开发出来，它需要先进的数值算法，实现和在计算机上的大规模计算。我们将尝试将两种最有前途的算法的关键优势结合在一起，即建立良好的图解蒙特卡罗方法和最近发现的算法松原集成（AMI）。这项新技术的产生将使物理学家能够可靠地描述和控制最具挑战性、也是最重要的强电子相关现象，这是以往任何先进方法都无法解决的一类问题。

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.