Electron-boson spectral density functions of cuprates obtained from optical spectra via machine learning

TL;DR

This paper introduces a machine learning approach to extract electron-boson spectral density functions from optical spectra in cuprates, offering improved robustness over traditional methods and enabling rapid analysis of noisy data.

Contribution

A novel machine learning method for extracting glue functions from optical spectra, outperforming traditional techniques in noise robustness.

Findings

MLA is more robust against noise than MEM.

Reliable glue functions were obtained from experimental data.

MLA can be applied to other inversion problems with noise.

Abstract

The electron-boson spectral density (or glue) function can be obtained from measured optical scattering rate by solving a generalized Allen formula, which relates the two quantities with an integral equation and is an inversion problem. Thus far, numerical approaches, such as the maximum entropy method (MEM) and the least squares fitting method, have been applied for solving the generalized Allen formula. Here, we developed a new method to obtain the glue functions from the optical scattering rate using a machine learning approach (MLA). We found that the MLA is more robust against random noise compared with the MEM. We applied the new developed MLA to experimentally measured optical scattering rates and obtained reliable glue functions in terms of their shapes including the amplitudes. We expect that the MLA can be a useful and rapid method for solving other inversion problems, which may contain random noise.