Causal optimization method for imaginary-time Green's functions in interacting electron systems

TL;DR

This paper introduces a causal optimization technique that enforces causality in numerical Green's function calculations for interacting electron systems, improving stability and accuracy in quantum many-body simulations.

Contribution

A novel causal optimization method that guarantees causality in Green's function computations, enhancing numerical stability and removing noncausal errors in many-body calculations.

Findings

Effective removal of noncausal errors in Green's functions.

Stabilization of Luttinger-Ward functional calculations.

Improved accuracy in dynamical mean-field theory simulations.

Abstract

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.