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Controlling Complex Langevin simulations of lattice models by boundary term analysis
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One reason for the well known fact that the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with abelian and non-abelian one-plaquette models, then we proceed to a Polyakov chain model and finally to high density QCD (HDQCD) and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.
Forward citations
Cited by 5 Pith papers
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Lefschetz thimble-inspired weight regularizations for complex Langevin simulations
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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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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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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Thermodynamic Diagnostics for Complex Langevin Simulations: The Role of Configurational Temperature
Configurational temperature from action gradients and Hessians offers a sensitive new correctness diagnostic for complex Langevin simulations, reproducing input temperature to 0.2-3% in 1D PT-symmetric models.
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