An improvement in complex Langevin dynamics from a view point of Lefschetz thimbles

Abstract

We develop a way of improving complex Langevin dynamics motivated by the Lefschetz-thimble decomposition of integrals. In our method, arbitrary observables of an original model with multiple Lefschetz thimbles are computed by a modified model with a single thimble. We apply our modification method to a one dimensional integral in which the naive implementation of the complex Langevin dynamics fails to reproduce the exact results due to the severe sign problem. We show that the toy model can be modified so that the new model consists of a single Lefschetz thimble. We find that correct results can be obtained by the improved complex Langevin dynamics.

7 pages, 7 figures

References in corpus (12)

• A Monte Carlo algorithm for simulating fermions on Lefschetz thimbles
• New insights into the problem with a singular drift term in the complex Langevin method
• Lefschetz-thimble analysis of the sign problem in one-site fermion model
• Structure of Lefschetz thimbles in simple fermionic systems
• Some remarks on Lefschetz thimbles and complex Langevin dynamics
• Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
• Full simulation of chiral Random Matrix Theory at non-zero chemical potential by Complex Langevin
• Thimble regularization at work: from toy models to chiral random matrix theories
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• Comparison of complex Langevin and mean field methods applied to effective Polyakov line models
• Complex saddle points and the sign problem in complex Langevin simulation
• Hamilton dynamics for the Lefschetz thimble integration akin to the complex Langevin method

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• Does the complex Langevin method give unbiased results?
• Complex saddle points and the sign problem in complex Langevin simulation
• One-dimensional QCD in thimble regularization
• Complex Langevin analysis of the spontaneous symmetry breaking in dimensionally reduced super Yang-Mills models
• Multi-flavor massless QED${}_2$ at finite densities via Lefschetz thimbles
• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
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• Modifying partition functions: a way to solve the sign problem
• Gauge invariant input to neural network for path optimization method
• Analytical studies of the complex Langevin equation with a Gaussian Ansatz and multiple solutions in the unstable region
• Testing a generalized cooling procedure in the complex Langevin simulation of chiral Random Matrix Theory
• Deep Learning of Fermion Sign Fluctuations
• Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
• Fermion Bag Approach for Massive Thirring Model at Finite Density
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Dynamical Compactification of Extra Dimensions in the Euclidean IKKT Matrix Model via Spontaneous Symmetry Breaking