Unification of the complex Langevin method and the Lefschetz-thimble method

Abstract

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.

8 pages, 12 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017), 18-24 June 2017, Granada, Spain

References in corpus (2)

• Complex Langevin dynamics and zeroes of the fermion determinant
• Combining the complex Langevin method and the generalized Lefschetz-thimble method

Cited by in corpus (3)

• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Control the model sign problem via path optimization method: Monte-Carlo approach to QCD effective model with Polyakov loop
• Application of the path optimization method to the sign problem in an effective model of QCD with a repulsive vector-type interaction