Lecture notes on Diagrammatic Monte Carlo for the Fr\"ohlich polaron.
This text originated from a number of lectures taught at various summer schools over the past two years, aiming to introduce the diagrammatic Monte Carlo method. These notes are intended as a detailed discussion on how to implement the diagrammatic Monte Carlo method for a physical system which is technically simple and where it works extremely well, namely the Fr\"ohlich polaron problem. They are not intended as a review on the physics of polarons, nor as a review of all problems where the method has been used. Sampling schemes for the Green function as well as the self-energy in the bare and skeleton (bold) expansion are disclosed in full detail. We discuss the Monte Carlo updates as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Sample codes are made available online. After working through these notes, the reader will be well equipped to explore the richness of the diagrammatic Monte Carlo method for quantum many-body systems.
Publisher URL: http://arxiv.org/abs/1711.03044