The sign problem and the Lefschetz thimble
Marco Cristoforetti (ECT), Francesco Di Renzo (Parma U., INFN,, Parma), Luigi Scorzato (ECT)
TL;DR
This paper discusses a novel method for addressing the sign problem in quantum field theory simulations by formulating the theory on Lefschetz thimbles, including a review and testing of the Aurora Monte Carlo algorithm.
Contribution
It introduces the application of Lefschetz thimbles to scalar field theories with sign problems and details the Aurora Monte Carlo algorithm for this purpose.
Findings
The formulation on Lefschetz thimbles is justified for scalar field theories.
The Aurora Monte Carlo algorithm is proposed and under testing.
The approach aims to mitigate the sign problem in QFT simulations.
Abstract
Recently, we have proposed a novel approach (arxiv:1205.3996) to deal with the sign problem that hinders Monte Carlo simulations of many quantum field theories (QFTs). The approach consists in formulating the QFT on a Lefschetz thimble. In this paper we concentrate on the application to a scalar field theory with a sign problem. In particular, we review the formulation and the justification of the approach, and we also describe the Aurora Monte Carlo algorithm that we are currently testing.
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