SciPost Phys. Lect. Notes 2 (2018) ·
published 11 June 2018
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· pdf
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.
