Computing real-time quantum path integrals on Sewed, almost-Lefschetz thimbles

Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders

Abstract

We present a method to compute real-time path integrals numerically, by Monte-Carlo sampling on near-Lefschetz thimbles. We present a collection of tools based on the Lefschetz thimble methods, which together provide an alternative to existing methods such as the Generalised thimble. These involve a convenient coordinate parameterization of the thimble, direct numerical integration along a radial coordinate into an effective path integral weight and locally deforming the Lefschetz thimble using its Gaussian (non-interacting theory) counterpart in a region about the critical point. We apply this to quantum mechanics, identify possible pitfalls and benefits, and benchmark its efficiency.

Citation

Mou, Z.-G., Saffin, P. M., & Tranberg, A. (2025). Computing real-time quantum path integrals on Sewed, almost-Lefschetz thimbles. Journal of High Energy Physics, 2025(3), Article 58. https://doi.org/10.1007/jhep03%282025%29058

• Journal Article Type: Article
• Acceptance Date: Feb 4, 2025
• Online Publication Date: Mar 7, 2025
• Publication Date: Mar 1, 2025
• Deposit Date: Mar 13, 2025
• Publicly Available Date: Mar 13, 2025
• Journal: Journal of High Energy Physics
• Electronic ISSN: 1029-8479
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 2025
• Issue: 3
• Article Number: 58
• DOI: https://doi.org/10.1007/jhep03%282025%29058
• Public URL: https://nottingham-repository.worktribe.com/output/46313566
• Publisher URL: https://link.springer.com/article/10.1007/JHEP03(2025)058