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Stability of complex Langevin dynamics in effective models
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The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.
Forward citations
Cited by 3 Pith papers
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A single compact Lefschetz thimble restores correct complex Langevin convergence, and a Dyson-Schwinger bias correction recovers the original expectation values.
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Diffusion models learn distributions generated by complex Langevin dynamics
Diffusion models reproduce the distributions sampled by complex Langevin dynamics in a Gaussian and a quartic toy model with complex mass.
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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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