Derivation of line shape function in the optical conductivity by a new diagram method

TL;DR

This paper introduces a new diagrammatic method, called the KC diagram method, for deriving line shape functions in optical conductivity, providing better physical insight and satisfying population criteria in electron-phonon systems.

Contribution

The paper presents a novel diagram method based on the Kang-Choi reduction identity for deriving optical conductivity line shapes, improving physical understanding and correctness over existing methods.

Findings

The KC diagram method satisfies the population criterion.

It provides a more intuitive understanding of quantum electron dynamics.

Results agree with the projection-reduction method for electron-phonon systems.

Abstract

A new diagram method to derive line shape function in the optical conductivity formula is introduced and the result obtained applying the method to an electron-phonon system is compared with that derived using the projection-reduction method. The result satisfies the population criterion, which states that the distribution functions for electrons and phonons should be combined in multiplicative forms, and gives physical intuition to quantum dynamics of electrons in a solid. This method can be called the "KC diagram" method because it originates from the proper application of the Kang-Choi reduction identity and a state-dependent projection operator.