A test on analytic continuation of thermal imaginary-time data

TL;DR

This paper tests a novel method for analytically continuing thermal imaginary-time data to real time, revealing its simplicity and potential for estimating transport coefficients, but also highlighting systematic errors and limitations.

Contribution

It provides an empirical evaluation of Cuniberti et al's method, demonstrating its practical implementation and identifying key challenges in error quantification.

Findings

Method is simple to implement

Allows qualitative estimates of transport coefficients

Systematic errors are difficult to quantify

Abstract

Some time ago, Cuniberti et al have proposed a novel method for analytically continuing thermal imaginary-time correlators to real time, which requires no model input and should be applicable with finite-precision data as well. Given that these assertions go against common wisdom, we report on a naive test of the method with an idealized example. We do encounter two problems, which we spell out in detail; this implies that systematic errors are difficult to quantify. On a more positive note, the method is simple to implement and allows for an empirical recipe by which a reasonable qualitative estimate for some transport coefficient may be obtained, if statistical errors of an ultraviolet-subtracted imaginary-time measurement can be reduced to roughly below the per mille level.