Numerical sign problem and the tempered Lefschetz thimble method

Abstract

The numerical sign problem is a major obstacle to the quantitative understanding of many important physical systems with first-principles calculations. Typical examples for such systems include finite-density QCD, strongly-correlated electron systems and frustrated spin systems, as well as the real-time dynamics of quantum systems. In this talk, we argue that the "tempered Lefschetz thimble method" (TLTM) [M. Fukuma and N. Umeda, arXiv:1703.00861] and its extension, the "worldvolume tempered Lefschetz thimble method" (WV-TLTM) [M. Fukuma and N. Matsumoto, arXiv:2012.08468], may be a reliable and versatile solution to the sign problem. We demonstrate the effectiveness of the algorithm by exemplifying a successful application of WV-TLTM to the Stephanov model, which is an important toy model of finite-density QCD. We also discuss the computational scaling of WV-TLTM.

Comments: 15 pages, 7 figures. Contribution to the proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2021) 29 August - 9 October 2021 Corfu, Greece