Abstract
One of the main challenges in simulations on Lefschetz thimbles is the computation of the relative weights of contributing thimbles. In this paper we propose a solution to that problem by means of computing those weights using a reweighting procedure. Besides we present recipes for finding parametrizations of thimbles and anti-thimbles for a given theory. Moreover, we study some approaches to combine the Lefschetz thimble method with the Complex Langevin evolution. Our numerical investigations are carried out by using toy models among which we consider a one-site z^4z4 model as well as a U(1)U(1) one-link model.
Highlights
C.3 we propose a combination of Lefschetz thimble and complex Langevin, which samples around all thimbles
We propose a new method based on Lefschetz thimbles for solving theories with a sign problem
We project a grid of points in the complex plane onto the thimbles – which requires the knowledge of the fixed points – to obtain a numerical parametrization
Summary
QCD at vanishing and finite temperature is one of the best tested theories in high energy physics. The first employs Monte Carlo simulations directly on the thimbles The latter continuously deforms the original integration path close to the actual thimbles to lessen the sign problem. One of the main problems with Monte Carlo simulations on Lefschetz thimbles is to determine the weights of the thimbles relative to each other This difficulty arises as the original path integral is decomposed into a sum of integrals over multiple thimbles. During the research for this paper we have developed many ideas to combine the Complex Langevin evolution and the Lefschetz Thimble method While none of those approaches lead to generally applicable algorithms, they still provide some useful insight into the structure of the models, we give some of those ideas and corresponding results in App. C
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
