J. Pawlowski, M. Scherzer, C. Schmidt, Felix Ziegler, F. Ziesch'e
{"title":"Lefschetz顶针的模拟测量理论","authors":"J. Pawlowski, M. Scherzer, C. Schmidt, Felix Ziegler, F. Ziesch'e","doi":"10.22323/1.363.0223","DOIUrl":null,"url":null,"abstract":"Lefschetz thimbles have been proposed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss pure abelian gauge theory with a complex coupling $\\beta$ and apply the concept of Generalized Lefschetz thimbles. We propose to simulate the theory on the union of the tangential manifolds to the thimbles. We construct a local Metropolis-type algorithm, that is constrained to a specific tangential manifold. We also discuss how, starting from this result, successive subleading tangential manifolds can be taken into account via a reweighting approach. We demonstrate the algorithm on $U(1)$ gauge theory in 1+1 dimensions and investigate the residual sign problem.","PeriodicalId":8440,"journal":{"name":"arXiv: High Energy Physics - Lattice","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Simulating gauge theories on Lefschetz Thimbles\",\"authors\":\"J. Pawlowski, M. Scherzer, C. Schmidt, Felix Ziegler, F. Ziesch'e\",\"doi\":\"10.22323/1.363.0223\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Lefschetz thimbles have been proposed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss pure abelian gauge theory with a complex coupling $\\\\beta$ and apply the concept of Generalized Lefschetz thimbles. We propose to simulate the theory on the union of the tangential manifolds to the thimbles. We construct a local Metropolis-type algorithm, that is constrained to a specific tangential manifold. We also discuss how, starting from this result, successive subleading tangential manifolds can be taken into account via a reweighting approach. We demonstrate the algorithm on $U(1)$ gauge theory in 1+1 dimensions and investigate the residual sign problem.\",\"PeriodicalId\":8440,\"journal\":{\"name\":\"arXiv: High Energy Physics - Lattice\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: High Energy Physics - Lattice\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22323/1.363.0223\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: High Energy Physics - Lattice","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22323/1.363.0223","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lefschetz thimbles have been proposed recently as a possible solution to the complex action problem (sign problem) in Monte Carlo simulations. Here we discuss pure abelian gauge theory with a complex coupling $\beta$ and apply the concept of Generalized Lefschetz thimbles. We propose to simulate the theory on the union of the tangential manifolds to the thimbles. We construct a local Metropolis-type algorithm, that is constrained to a specific tangential manifold. We also discuss how, starting from this result, successive subleading tangential manifolds can be taken into account via a reweighting approach. We demonstrate the algorithm on $U(1)$ gauge theory in 1+1 dimensions and investigate the residual sign problem.