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arXiv · 1808.05187

Complex Langevin and boundary terms

Manuel Scherzer·Erhard Seiler·Dénes Sexty·Ion-Olimpiu Stamatescu
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Abstract

As is well known the Complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit. We identified one reason for this long ago: 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, we analyze the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. We also show how some simple modification stabilizes the CL process in such a way that it can produce results agreeing with direct integration. Besides explicitly demonstrating the connection between boundary terms and correct convergence our analysis also suggests a correctness criterion which could be applied in realistic lattice simulations.

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Manuel Scherzer, Erhard Seiler, Dénes Sexty, Ion-Olimpiu Stamatescu. 2018-08-15. Complex Langevin and boundary terms. https://doi.org/10.1103/physrevd.99.014512

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