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Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
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Complex Langevin (CL) is a computational method to circumvent the numerical sign problem with applications in finite-density quantum chromodynamics and the real-time dynamics of quantum field theories. It has long been known that, depending on the simulated system, CL does not always converge correctly. In this work, we provide numerical evidence that the success or failure of the complex Langevin method is deeply tied to the Lefschetz thimble structure of the simulated system. This is demonstrated by constructing weight function regularizations that deform the thimbles of systems with compact domains. Our results indicate that CL converges correctly when the regularized system exhibits a single relevant compact thimble. We introduce a bias correction to retrieve the values of the original theory for parameter sets where a direct complex Langevin approach fails. The effectiveness of this method is illustrated using several toy models, including the cosine model and the SU(2) and SU(3) Polyakov chains. Finally, we discuss the opportunities and limitations of this regularization approach for lattice field theories.
Forward citations
Cited by 4 Pith papers
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Designing weight regularizations based on Lefschetz thimbles to stabilize complex Langevin
A regularization inspired by Lefschetz thimbles stabilizes complex Langevin simulations in toy models, with a bias-correction step that restores the original expectation values.
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Complex Langevin results in one- and two-dimensional toy models match a linear combination of integration cycles when boundary terms vanish, and the kernel choice controls which cycles contribute.
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Energy-based diffusion models trained on complex Langevin data produce an explicit energy function for the sampled distribution, enabling MCMC without re-simulation.
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