Diagrammatic Monte Carlo Method in Quantum Statistics

University Of Massachusetts Amherst, Amherst MA

Investigators

Abstract

This grant supports further work on some recently discovered algorithms for numerical work in quantum magnetism and on the properties of strongly correlated electrons. The two methods, originally discovered by the PI and collaborators, are diagrammatic Monte Carlo (DMC) and Worm-algorithm. The former involves direct simulation of diagrammatic expansions while the latter is a novel simulation strategy involving extended configuration space. The two strategies make it possible to address various problems which have remained unsolved so far. They are also an improvement in efficiency, in both speed and accuracy for problems which have been studied by other means. Finally, these techniques are associated with either new representation (momentum instead of coordinate, grand canonical instead of canonical ensemble) or simulation of new entities (e.g. Green functions, which allow on to extract elementary excitation spectrum or even kinetic coefficients). The specific problems where these techniques will be applied, include, polarons and exciton-polaron interaction in semiconductors, holes in quantum Antiferromagnets and quantum gases at ultra low temperatures. %%% This grant is being awarded for further development of two new numerical techniques developed by this PI. These are diagrammatic-Monte-Carlo methods and Worm algorithm. These techniques can allow one to numerically attack problems which have so far resisted a solution or even a partial understanding. The techniques are believed to be both accurate and extremely fast. They will be used to study a variety of so far unsolved problems in the properties of novel materials. ***