Analytical continuation of imaginary axis data for optical conductivity

TL;DR

This paper compares various analytical continuation methods, including MaxEnt, SVD, sampling, and Pade, for converting spectral data from imaginary to real frequencies in optical conductivity analysis, highlighting their relative accuracy.

Contribution

It provides a systematic comparison of multiple analytical continuation techniques and introduces a modified MaxEnt approach with batch processing for improved results.

Findings

SVD, sampling, and modified MaxEnt yield comparable accuracy

Pade approximation is generally less reliable

Batch processing enhances MaxEnt performance

Abstract

We compare different methods for performing analytical continuation of spectral data from the imaginary time or frequency axis to the real frequency axis for the optical conductivity sigma(omega). We compare the maximum entropy (MaxEnt), singular value decomposition (SVD), sampling and Pade methods for analytical continuation. We also study two direct methods for obtaining sigma(0). For the MaxEnt approach we focus on a recent modification. The data are split up in batches, a separate MaxEnt calculation is done for each batch and the results are averaged. For the problems studied here, we find that typically the SVD, sampling and modified MaxEnt methods give comparable accuracy, while the Pade approximation is usually less reliable.