Numerical sign problem and the tempered Lefschetz thimble method

TL;DR

The paper discusses the tempered Lefschetz thimble method and its extension as promising approaches to overcoming the numerical sign problem in complex quantum systems, demonstrated through application to the Stephanov model.

Contribution

It introduces and evaluates the effectiveness of the WV-TLTM method in addressing the sign problem in finite-density QCD models.

Findings

WV-TLTM successfully applied to the Stephanov model

Demonstrates computational scaling of WV-TLTM

Proposes WV-TLTM as a reliable solution to the sign problem

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.