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The complex Langevin method and the generalized Lefschetz-thimble method are two closely related approaches to the sign problem, which are both based on complexification of the original dynamical variables. The former can be viewed as a generalization of the stochastic quantization using the Langevin equation, whereas the latter is a deformation of the integration contour using the so-called holomorphic gradient flow. In order to clarify their relationship, we propose a formulation which combines the two methods by applying the former method to the real variables that parametrize the deformed integration contour in the latter method. Thr
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
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
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the gauge cooli
In recent years, there has been remarkable progress in theoretical justification of the complex Langevin method, which is a promising method for evading the sign problem in the path integral with a complex weight. There still remains, however, an iss
The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in some cases, w