  We develop a causal optimization method that ensures causality in numerical
calculations of Green's functions in interacting electron systems. Our method
removes noncausality of numerical data by finding causal functions closest to
the data. By testing our method with an exactly calculable model and applying
it to practical dynamical mean-field calculations, we find that
intermediate-frequency behaviors of Green's functions are determined solely by
causality, and noncausal statistical errors are removed very efficiently.
Furthermore, we demonstrate that numerical calculations of the physical branch
of the Luttinger-Ward functional can be stabilized by ensuring causality of the
noninteracting Green's function. Our method and findings provide a basis for
improving stability and efficiency of numerical simulations of quantum
many-body systems.
