Unification of the complex Langevin method and the Lefschetzthimble method
KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
2 Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
3 Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan
* Speaker, e-mail: firstname.lastname@example.org
Published online: 26 March 2018
Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share the idea of complexifying the dynamical variables, but their relationship has not been clear. Here we propose a unified formulation, in which the sign problem is taken care of by both the Langevin dynamics and the holomorphic gradient flow. We apply our formulation to a simple model in three different ways and show that one of them interpolates the two methods by changing the flow time.
© The Authors, published by EDP Sciences, 2018
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