Lecture notes on Diagrammatic Monte Carlo for the Fröhlich polaron
JG and Lode Pollet
published in SciPost Phys. Lect. Notes 2
Abstract
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 Fröhlich polaron problem. 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, possible implementations in terms of common data structures, as well as techniques on how to perform the Fourier transforms for functions with discontinuities. Control over the variety of parameters, especially in the bold scheme, is demonstrated. Sample codes are made available online along with extensive documentation. Towards the end, we discuss various extensions of the method and their applications. 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.
The DiagQMC codes described in these notes are available under an open-source license (GPLv3) on the LRZ GitLab server.
Refer to the README for detailed instructions on building and running our
codes. Feel free to reach out in case of problems.