University of Massachusetts

Title:Diagrammatic Monte Carlo and Worm algorithm: From Polarons and Polymers to Interacting Bosons.

Abstract: I will discuss two numerical techniques which drastically improve the accuracy and efficiency of simulations for problems with complex topology of the configuration space, or when a large number of continuous variables are involved. Worm Algorithm is based on the idea of updating a tangle of continuous paths (worldlines, trajectories, polymer chains, etc.) exclusively through the creation/removal of a disconnected path with two ''loose'' ends and the stochastic motion of the end points. Diagrammatic Monte Carlo solves any problem where the answer is specified in terms of a convergent positive-definite series of integrals (or sums), and is a generic prescription of how to organize a systematic-error-free Metropolis-type process that samples the corresponding series without explicitly taking the integrals over the internal variables in each particular term. Applications include polarons, excitons, holes in antiferromagnets, polymers, quantum dots, interacting Bose and spin systems, as well a number of classical statistical models.