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The complex Langevin method (CLM) provides a promising way to perform thepath integral with a complex action using a stochastic equation forcomplexified dynamical variables. It is known, however, that the method giveswrong results in some cases, while it works, for instance, in finite densityQCD in the deconfinement phase or in the heavy dense limit. Here we revisit theargument for justification of the CLM and point out a subtlety in using thetime-evolved observables, which play a crucial role in the argument. Thissubtlety requires that the probability distribution of the drift term shouldfall off exponentially or faster at large magnitude. We demonstrate our claimin some examples such as chiral Random Matrix Theory and show that ourcriterion is indeed useful in judging whether the results obtained by the CLMare trustable or not.

On the condition for correct convergence in the complex Langevin method