Causal projection approach for imaginary-time quantum many-body simulations

In many-body physics, causality often refers to positive semidefiniteness of electronic spectral function. However, most numerical simulations of many-particle systems are performed in imaginary time, without any explicit consideration for causality. In this work, we present a causal projection approach which projects an imaginary-time numerical function onto a space of functions satisfying causality. Using this method, we can impose causality in imaginary-time many-body calculations. Applying this method to finite and statistical calculations, we demonstrate that causality determines intermediate-frequency behaviors smoothly, excluding unphysical statistical errors efficiently. Furthermore, we show that our causal projection method can suppress unphysical branches of the Luttinger-Ward functional.