New generation of Diagrammatic Monte Carlo methods

EPSRC : Connor Lenihan : EP/R513064/1

The 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.