The Complex Langevin method: When can it be trusted?
Gert Aarts (Swansea University), Erhard Seiler (MPI Munich) and, Ion-Olimpiu Stamatescu (Heidelberg University, FEST, Heidelberg)
TL;DR
This paper critically examines the reliability of the complex Langevin method for solving sign problems, providing a formal correctness analysis, identifying mathematical loopholes, and offering practical guidance through simple examples.
Contribution
It offers a formal derivation of the method's correctness, highlights mathematical loopholes, and provides practical suggestions based on simple examples.
Findings
Formal derivation of complex Langevin correctness
Identification of mathematical loopholes
Practical application suggestions
Abstract
We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.